diff --git a/src/griffe/agents/inspector.py b/src/griffe/agents/inspector.py
index eec072e0..636d61da 100644
--- a/src/griffe/agents/inspector.py
+++ b/src/griffe/agents/inspector.py
@@ -35,6 +35,7 @@
 from griffe.expressions import safe_get_annotation
 from griffe.extensions.base import Extensions, load_extensions
 from griffe.importer import dynamic_import
+from griffe.logger import get_logger
 
 if TYPE_CHECKING:
     from pathlib import Path
@@ -43,6 +44,7 @@
     from griffe.expressions import Expr
 
 
+logger = get_logger(__name__)
 empty = Signature.empty
 
 
@@ -218,9 +220,34 @@ def generic_inspect(self, node: ObjectNode) -> None:
             before_inspector.inspect(node)
 
         for child in node.children:
-            target_path = child.alias_target_path
-            if target_path:
-                self.current.set_member(child.name, Alias(child.name, target_path))
+            if target_path := child.alias_target_path:
+                # If the child is an actual submodule of the current module,
+                # and has no `__file__` set, we won't find it on the disk so we must inspect it now.
+                # For that we instantiate a new inspector and use it to inspect the submodule,
+                # then assign the submodule as member of the current module.
+                # If the submodule has a `__file__` set, the loader should find it on the disk,
+                # so we skip it here (no member, no alias, just skip it).
+                if child.is_module and target_path == f"{self.current.path}.{child.name}":
+                    if not hasattr(child.obj, "__file__"):
+                        logger.debug(f"Module {target_path} is not discoverable on disk, inspecting right now")
+                        inspector = Inspector(
+                            child.name,
+                            filepath=None,
+                            parent=self.current.module,
+                            extensions=self.extensions,
+                            docstring_parser=self.docstring_parser,
+                            docstring_options=self.docstring_options,
+                            lines_collection=self.lines_collection,
+                            modules_collection=self.modules_collection,
+                        )
+                        try:
+                            inspector.inspect_module(child)
+                        finally:
+                            self.extensions.attach_inspector(self)
+                        self.current.set_member(child.name, inspector.current.module)
+                # Otherwise, alias the object.
+                else:
+                    self.current.set_member(child.name, Alias(child.name, target_path))
             else:
                 self.inspect(child)
 
diff --git a/tests/test_inspector.py b/tests/test_inspector.py
index 3b22ab48..a527c083 100644
--- a/tests/test_inspector.py
+++ b/tests/test_inspector.py
@@ -110,3 +110,40 @@ def test_inspecting_package_and_module_with_same_names() -> None:
     with temporary_pypackage("package", {"package.py": "a = 0"}) as tmp_package:
         inspect("package.package", filepath=tmp_package.path / "package.py", import_paths=[tmp_package.tmpdir])
     _clear_sys_modules("package")
+
+
+def test_inspecting_module_with_submodules() -> None:
+    """Inspecting a module shouldn't register any of its submodules if they're not imported."""
+    with temporary_pypackage("pkg", ["mod.py"]) as tmp_package:
+        pkg = inspect("pkg", filepath=tmp_package.path / "__init__.py")
+    assert "mod" not in pkg.members
+    _clear_sys_modules("pkg")
+
+
+def test_inspecting_module_with_imported_submodules() -> None:
+    """When inspecting a package on the disk, direct submodules should be skipped entirely."""
+    with temporary_pypackage(
+        "pkg",
+        {
+            "__init__.py": "from pkg import subpkg\nfrom pkg.subpkg import mod",
+            "subpkg/__init__.py": "a = 0",
+            "subpkg/mod.py": "b = 0",
+        },
+    ) as tmp_package:
+        pkg = inspect("pkg", filepath=tmp_package.path / "__init__.py")
+    assert "subpkg" not in pkg.members
+    assert "mod" in pkg.members
+    assert pkg["mod"].is_alias
+    assert pkg["mod"].target_path == "pkg.subpkg.mod"
+    _clear_sys_modules("pkg")
+
+
+def test_inspecting_objects_from_private_builtin_stdlib_moduless() -> None:
+    """Inspect objects from private built-in modules in the standard library."""
+    ast = inspect("ast")
+    assert "Assign" in ast.members
+    assert not ast["Assign"].is_alias
+
+    ast = inspect("_ast")
+    assert "Assign" in ast.members
+    assert not ast["Assign"].is_alias