diff --git a/src/poetry/utils/env/base_env.py b/src/poetry/utils/env/base_env.py
index 1a8ff54bd26..935b28bb636 100644
--- a/src/poetry/utils/env/base_env.py
+++ b/src/poetry/utils/env/base_env.py
@@ -80,6 +80,7 @@ def __init__(self, path: Path, base: Path | None = None) -> None:
 
         self._site_packages: SitePackages | None = None
         self._supported_tags: list[Tag] | None = None
+        self._supported_tags_set: set[Tag] | None = None
         self._purelib: Path | None = None
         self._platlib: Path | None = None
         self._script_dirs: list[Path] | None = None
@@ -359,6 +360,13 @@ def supported_tags(self) -> list[Tag]:
 
         return self._supported_tags
 
+    @property
+    def supported_tags_set(self) -> set[Tag]:
+        if self._supported_tags_set is None:
+            self._supported_tags_set = set(self.supported_tags)
+
+        return self._supported_tags_set
+
     @classmethod
     def get_base_prefix(cls) -> Path:
         real_prefix = getattr(sys, "real_prefix", None)
diff --git a/src/poetry/utils/env/mock_env.py b/src/poetry/utils/env/mock_env.py
index 0ffdc72eda3..aaaa75b209f 100644
--- a/src/poetry/utils/env/mock_env.py
+++ b/src/poetry/utils/env/mock_env.py
@@ -41,6 +41,9 @@ def __init__(
         self._sys_path = sys_path
         self._mock_marker_env = marker_env
         self._supported_tags = supported_tags
+        # _supported_tags_set should not be set at this point.
+        # We reset it after setting _supported_tags just to be sure.
+        self._supported_tags_set = None
 
     @property
     def platform(self) -> str:
diff --git a/src/poetry/utils/wheel.py b/src/poetry/utils/wheel.py
index bb4a70b7907..a50be4ba79b 100644
--- a/src/poetry/utils/wheel.py
+++ b/src/poetry/utils/wheel.py
@@ -44,4 +44,4 @@ def get_minimum_supported_index(self, tags: list[Tag]) -> int | None:
         return min(indexes) if indexes else None
 
     def is_supported_by_environment(self, env: Env) -> bool:
-        return bool(set(env.supported_tags).intersection(self.tags))
+        return not self.tags.isdisjoint(env.supported_tags_set)
diff --git a/tests/utils/test_wheel.py b/tests/utils/test_wheel.py
new file mode 100644
index 00000000000..5248e96d206
--- /dev/null
+++ b/tests/utils/test_wheel.py
@@ -0,0 +1,36 @@
+from __future__ import annotations
+
+import pytest
+
+from packaging.tags import Tag
+
+from poetry.utils.env import MockEnv
+from poetry.utils.wheel import Wheel
+
+
+@pytest.mark.parametrize(
+    ("filename", "supported_tags", "expected"),
+    [
+        ("demo-1.0.0-py3-none-any.whl", [Tag("py3", "none", "any")], True),
+        ("demo-1.0.0-cp312-cp312-win_amd64.whl", [Tag("py3", "none", "any")], False),
+        ("demo-1.0.0-py3-none-any.whl", [], False),
+        (
+            "demo-1.0.0-py3-none-any.whl",
+            [Tag("cp310", "none", "any"), Tag("py3", "none", "any")],
+            True,
+        ),
+    ],
+)
+def test_wheel_is_supported_by_environment(
+    filename: str, supported_tags: list[Tag], expected: bool
+) -> None:
+    env = MockEnv(supported_tags=supported_tags)
+
+    assert Wheel(filename).is_supported_by_environment(env) is expected
+
+
+def test_env_supported_tags_set_is_cached() -> None:
+    env = MockEnv(supported_tags=[Tag("py3", "none", "any")])
+
+    assert env.supported_tags_set == set(env.supported_tags)
+    assert env.supported_tags_set is env.supported_tags_set