diff --git a/src/pip/_internal/utils/misc.py b/src/pip/_internal/utils/misc.py
index 05dc2339443fc2777608f81f337302fa1d4d02d5..cb470f760a5b0cc0ea1947d3757c433138ee045c 100644
--- a/src/pip/_internal/utils/misc.py
+++ b/src/pip/_internal/utils/misc.py
@@ -45,13 +45,23 @@ else:
 
 if MYPY_CHECK_RUNNING:
     from typing import (
-        Optional, Tuple, Iterable, List, Match, Union, Any, Mapping, Text,
-        AnyStr, Container
+        Any, AnyStr, Container, Iterable, List, Mapping, Match, Optional, Text,
+        Union,
     )
     from pip._vendor.pkg_resources import Distribution
     from pip._internal.models.link import Link
     from pip._internal.utils.ui import SpinnerInterface
 
+try:
+    from typing import cast, Tuple
+    VersionInfo = Tuple[int, int, int]
+except ImportError:
+    # typing's cast() isn't supported in code comments, so we need to
+    # define a dummy, no-op version.
+    def cast(typ, val):
+        return val
+    VersionInfo = None
+
 
 __all__ = ['rmtree', 'display_path', 'backup_dir',
            'ask', 'splitext',
@@ -94,6 +104,29 @@ except ImportError:
     logger.debug('lzma module is not available')
 
 
+def normalize_version_info(py_version_info):
+    # type: (Optional[Tuple[int, ...]]) -> Optional[Tuple[int, int, int]]
+    """
+    Convert a tuple of ints representing a Python version to one of length
+    three.
+
+    :param py_version_info: a tuple of ints representing a Python version,
+        or None to specify no version. The tuple can have any length.
+
+    :return: a tuple of length three if `py_version_info` is non-None.
+        Otherwise, return `py_version_info` unchanged (i.e. None).
+    """
+    if py_version_info is None:
+        return None
+
+    if len(py_version_info) < 3:
+        py_version_info += (3 - len(py_version_info)) * (0,)
+    elif len(py_version_info) > 3:
+        py_version_info = py_version_info[:3]
+
+    return cast(VersionInfo, py_version_info)
+
+
 def ensure_dir(path):
     # type: (AnyStr) -> None
     """os.path.makedirs without EEXIST."""
diff --git a/tests/unit/test_utils.py b/tests/unit/test_utils.py
index a4550bcfed37f5732def5b9b5614bf89541b9d7a..4a8498bda48e20374ed3b3ed6a45141f8a75e89b 100644
--- a/tests/unit/test_utils.py
+++ b/tests/unit/test_utils.py
@@ -29,8 +29,9 @@ from pip._internal.utils.glibc import check_glibc_version
 from pip._internal.utils.hashes import Hashes, MissingHashes
 from pip._internal.utils.misc import (
     call_subprocess, egg_link_path, ensure_dir, format_command_args,
-    get_installed_distributions, get_prog, normalize_path, path_to_url,
-    redact_netloc, redact_password_from_url, remove_auth_from_url, rmtree,
+    get_installed_distributions, get_prog, normalize_path,
+    normalize_version_info, path_to_url, redact_netloc,
+    redact_password_from_url, remove_auth_from_url, rmtree,
     split_auth_from_netloc, split_auth_netloc_from_url, untar_file, unzip_file,
 )
 from pip._internal.utils.temp_dir import AdjacentTempDirectory, TempDirectory
@@ -700,6 +701,19 @@ class TestGlibc(object):
                     assert False
 
 
+@pytest.mark.parametrize('version_info, expected', [
+    (None, None),
+    ((), (0, 0, 0)),
+    ((3, ), (3, 0, 0)),
+    ((3, 6), (3, 6, 0)),
+    ((3, 6, 2), (3, 6, 2)),
+    ((3, 6, 2, 4), (3, 6, 2)),
+])
+def test_normalize_version_info(version_info, expected):
+    actual = normalize_version_info(version_info)
+    assert actual == expected
+
+
 class TestGetProg(object):
 
     @pytest.mark.parametrize(