diff --git a/micropip/_utils.py b/micropip/_utils.py
index 9abab9d..8bbc62e 100644
--- a/micropip/_utils.py
+++ b/micropip/_utils.py
@@ -117,7 +117,7 @@ def best_compatible_tag_index(tags: frozenset[Tag]) -> int | None:
     return None
 
 
-def is_package_compatible(filename: str) -> bool:
+def is_package_compatible(filename: str) -> tuple[bool, int | None]:
     """
     Check if a package is compatible with the current platform.
 
@@ -128,17 +128,15 @@ def is_package_compatible(filename: str) -> bool:
     """
 
     if not filename.endswith(".whl"):
-        return False
-
-    if filename.endswith("py3-none-any.whl"):
-        return True
+        return False, None
 
     try:
         tags = parse_tags(filename)
     except (InvalidVersion, InvalidWheelFilename):
-        return False
+        return False, None
 
-    return best_compatible_tag_index(tags) is not None
+    tag_index = best_compatible_tag_index(tags)
+    return (tag_index is not None), tag_index
 
 
 def check_compatible(filename: str) -> None:
@@ -146,7 +144,7 @@ def check_compatible(filename: str) -> None:
     Check if a package is compatible with the current platform.
     If not, raise an exception with a error message that explains why.
     """
-    compatible = is_package_compatible(filename)
+    compatible, _ = is_package_compatible(filename)
     if compatible:
         return
 
diff --git a/micropip/package_index.py b/micropip/package_index.py
index c7e4d08..b433a26 100644
--- a/micropip/package_index.py
+++ b/micropip/package_index.py
@@ -147,7 +147,7 @@ def _compatible_wheels(
 
             # Checking compatibility takes a bit of time,
             # so we use a generator to avoid doing it for all files.
-            compatible = is_package_compatible(filename)
+            compatible, tag_index = is_package_compatible(filename)
             if not compatible:
                 continue
 
@@ -177,6 +177,7 @@ def _compatible_wheels(
                 size=size,
                 core_metadata=core_metadata,
                 yanked_reason=yanked_reason,
+                best_tag_index=tag_index,
             )
 
     @classmethod
diff --git a/micropip/transaction.py b/micropip/transaction.py
index 3f6f1f8..abadffb 100644
--- a/micropip/transaction.py
+++ b/micropip/transaction.py
@@ -10,7 +10,6 @@
 from . import package_index
 from ._compat import CompatibilityLayer
 from ._utils import (
-    best_compatible_tag_index,
     check_compatible,
     constrain_requirement,
     validate_constraints,
@@ -413,7 +412,7 @@ def _find_best_wheel(wheels: Iterable[WheelInfo]) -> WheelInfo | None:
     best_wheel = None
     best_tag_index = float("infinity")
     for wheel in wheels:
-        tag_index = best_compatible_tag_index(wheel.tags)
+        tag_index = wheel.best_tag_index
         if tag_index is not None and tag_index < best_tag_index:
             best_wheel = wheel
             best_tag_index = tag_index
diff --git a/micropip/wheelinfo.py b/micropip/wheelinfo.py
index d545dad..43cf378 100644
--- a/micropip/wheelinfo.py
+++ b/micropip/wheelinfo.py
@@ -13,7 +13,7 @@
     loadedPackages,
     to_js,
 )
-from ._utils import parse_wheel_filename
+from ._utils import best_compatible_tag_index, parse_wheel_filename
 from ._vendored.packaging.src.packaging.requirements import Requirement
 from ._vendored.packaging.src.packaging.tags import Tag
 from ._vendored.packaging.src.packaging.version import Version
@@ -47,6 +47,7 @@ class WheelInfo:
     yanked_reason: str | bool = (
         False  # Whether the wheel has been yanked and the reason (if given) (PEP-592)
     )
+    _best_tag_index: int | None = field(default=None, repr=False, compare=False)
 
     # Fields below are only available after downloading the wheel, i.e. after calling `download()`.
 
@@ -62,6 +63,15 @@ def __post_init__(self):
         self.metadata_url = self.url + ".metadata"
         self.yanked = bool(self.yanked_reason)
 
+    @property
+    def best_tag_index(self) -> int | None:
+        """
+        Returns an index if a compatible tag exists, otherwise None.
+        """
+        if self._best_tag_index is None:
+            self._best_tag_index = best_compatible_tag_index(self.tags)
+        return self._best_tag_index
+
     @classmethod
     def from_url(cls, url: str) -> "WheelInfo":
         """Parse wheels URL and extract available metadata
@@ -101,6 +111,7 @@ def from_package_index(
         size: int | None,
         core_metadata: DistributionMetadata = None,
         yanked_reason: str | bool = False,
+        best_tag_index: int | None = None,
     ) -> "WheelInfo":
         """Extract available metadata from response received from package index"""
         parsed_url = urlparse(url)
@@ -118,6 +129,7 @@ def from_package_index(
             size=size,
             core_metadata=core_metadata,
             yanked_reason=yanked_reason,
+            _best_tag_index=best_tag_index,
         )
 
     async def install(self, target: Path) -> None: