diff --git a/doc/en/_crossrefcheck.py b/doc/en/_crossrefcheck.py
new file mode 100644
index 00000000000..3a594951647
--- /dev/null
+++ b/doc/en/_crossrefcheck.py
@@ -0,0 +1,169 @@
+import sys
+from typing import Any
+from typing import cast
+from typing import Iterable
+from typing import Iterator
+from typing import NamedTuple
+from typing import TYPE_CHECKING
+
+import docutils.nodes
+import sphinx.builders.dummy
+import sphinx.transforms.post_transforms
+import sphinx.util.logging
+import sphinx.util.nodes
+
+
+if TYPE_CHECKING:
+    import sphinx.application
+    import sphinx.domains
+
+if sys.version_info >= (3, 9):
+    Inventory = dict[str, dict[str, tuple[str, str, str, str]]]
+else:
+    from typing import Dict, Tuple
+
+    Inventory = Dict[str, Dict[str, Tuple[str, str, str, str]]]
+
+
+logger = sphinx.util.logging.getLogger(__name__)
+
+
+class URIInfo(NamedTuple):
+    uri: str
+    document_name: str
+    line_number: int
+
+
+class LinkCollector(sphinx.transforms.post_transforms.SphinxPostTransform):
+    """
+    Traverse the document and collect all ``reference`` nodes that do not have the ``internal`` attribute set.
+
+    Typically, they will look like this:
+
+    .. code-block::
+
+       <reference name="link text" refuri="https://uri">link text, maybe further styled</reference>
+
+    We know those were not generated by Sphinx because they are missing the ``internal`` attribute.
+
+    This transform doesn't actually modify the document tree, only collecting stuff.
+    """
+
+    builders = ("crossrefcheck",)
+    default_priority = 900
+
+    def run(self, **kwargs: Any) -> None:
+        builder = cast(ExternalLinkChecker, self.app.builder)
+
+        for refnode in self.document.traverse(docutils.nodes.reference):
+            if "internal" in refnode or "refuri" not in refnode:
+                continue
+            uri = refnode["refuri"]
+            lineno = sphinx.util.nodes.get_node_line(refnode)
+
+            uri_info = URIInfo(uri, self.env.docname, lineno)
+            builder.uris.append(uri_info)
+
+
+class ExternalLinkChecker(sphinx.builders.dummy.DummyBuilder):
+    """
+    Custom builder that does not build anything, only analyzes the built result.
+
+    It is invoked when the user selects ``crossrefcheck`` as builder name
+    in the terminal:
+
+    .. code-block:: sh
+
+       $ sphinx-build -b crossrefcheck doc/en/ build
+
+    For every link not generated by Sphinx, it compares whether it matches
+    an inventory URL configured in ``intersphinx_mapping`` and warns if the
+    link can be replaced by an cross-reference.
+
+    .. note:: The matching is done by simply comparing URLs as strings
+       via ``str.startswith``. This means that with e.g. ``x`` project
+       configured as
+
+       .. code-block:: python
+
+          intersphinx_mapping = {
+              "x": ("https://x.readthedocs.io/en/stable", None),
+          }
+
+       no warning will be emitted for links ``https://x.readthedocs.io/en/latest``
+       or ``https://x.readthedocs.io/de/stable``.
+
+       Those links can be included by adding the missing docs
+       for ``x`` to ``intersphinx_mapping``:
+
+       .. code-block:: python
+
+          intersphinx_mapping = {
+              "x": ("https://x.readthedocs.io/en/stable", None),
+              "x-dev": ("https://x.readthedocs.io/en/latest", None),
+              "x-german": ("https://x.readthedocs.io/de/stable", None),
+          }
+
+    """
+
+    name = "crossrefcheck"
+
+    def __init__(self, app: "sphinx.application.Sphinx") -> None:
+        super().__init__(app)
+        self.uris: list[URIInfo] = []
+
+    def finish(self) -> None:
+        intersphinx_cache = getattr(self.app.env, "intersphinx_cache", dict())
+        for uri_info in self.uris:
+            for inventory_uri, (
+                inventory_name,
+                _,
+                inventory,
+            ) in intersphinx_cache.items():
+                if uri_info.uri.startswith(inventory_uri):
+                    # build a replacement suggestion
+                    try:
+                        replacement = next(
+                            replacements(
+                                uri_info.uri, inventory, self.app.env.domains.values()
+                            )
+                        )
+                        suggestion = f"try using {replacement!r} instead"
+                    except StopIteration:
+                        suggestion = "no suggestion"
+
+                    location = (uri_info.document_name, uri_info.line_number)
+                    logger.warning(
+                        "hardcoded link %r could be replaced by a cross-reference to %r inventory (%s)",
+                        uri_info.uri,
+                        inventory_name,
+                        suggestion,
+                        location=location,
+                    )
+
+
+def replacements(
+    uri: str, inventory: Inventory, domains: Iterable["sphinx.domains.Domain"]
+) -> Iterator[str]:
+    """
+    Create a crossreference to replace hardcoded ``uri``.
+
+    This is straightforward: search the given inventory
+    for an entry that points to the ``uri`` and build
+    a ReST markup that should replace ``uri`` with a crossref.
+    """
+    for key, entries in inventory.items():
+        domain_name, directive_type = key.split(":")
+        for target, (_, _, target_uri, _) in entries.items():
+            if uri == target_uri:
+                role = "any"
+                for domain in domains:
+                    if domain_name == domain.name:
+                        role = domain.role_for_objtype(directive_type) or "any"
+                        yield f":{domain_name}:{role}:`{target}`"
+
+
+def setup(app: "sphinx.application.Sphinx") -> None:
+    """Register this extension."""
+    app.add_builder(ExternalLinkChecker)
+    app.add_post_transform(LinkCollector)
diff --git a/doc/en/conf.py b/doc/en/conf.py
index 70b9c93fe40..21ff8b0adc8 100644
--- a/doc/en/conf.py
+++ b/doc/en/conf.py
@@ -32,7 +32,7 @@
 # If extensions (or modules to document with autodoc) are in another directory,
 # add these directories to sys.path here. If the directory is relative to the
 # documentation root, use os.path.abspath to make it absolute, like shown here.
-# sys.path.insert(0, os.path.abspath('.'))
+sys.path.insert(0, os.path.abspath("."))
 
 autodoc_member_order = "bysource"
 autodoc_typehints = "description"
@@ -55,6 +55,7 @@
     "sphinx.ext.viewcode",
     "sphinx_removed_in",
     "sphinxcontrib_trio",
+    "_crossrefcheck",
 ]
 
 # Add any paths that contain templates here, relative to this directory.
diff --git a/tox.ini b/tox.ini
index c6dd3f477ee..30fb98b1375 100644
--- a/tox.ini
+++ b/tox.ini
@@ -16,6 +16,7 @@ envlist =
     py37-freeze
     docs
     docs-checklinks
+    docs-checkcrossrefs
 
 [testenv]
 commands =
@@ -80,6 +81,14 @@ deps = -r{toxinidir}/doc/en/requirements.txt
 commands =
     sphinx-build -W -q --keep-going -b linkcheck . _build
 
+[testenv:docs-checkcrossrefs]
+basepython = python3
+usedevelop = True
+changedir = doc/en
+deps = -r{toxinidir}/doc/en/requirements.txt
+commands =
+    sphinx-build -W -q --keep-going -b crossrefcheck . _build
+
 [testenv:regen]
 changedir = doc/en
 basepython = python3