diff --git a/nox/command.py b/nox/command.py
index e49e2b55..671875cb 100644
--- a/nox/command.py
+++ b/nox/command.py
@@ -83,7 +83,7 @@ def run(
     log: bool = True,
     external: ExternalType = False,
     stdout: int | IO[str] | None = None,
-    stderr: int | IO[str] = subprocess.STDOUT,
+    stderr: int | IO[str] | None = subprocess.STDOUT,
     interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
     terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
 ) -> str | bool:
diff --git a/nox/popen.py b/nox/popen.py
index f9751461..5f32a9e9 100644
--- a/nox/popen.py
+++ b/nox/popen.py
@@ -66,7 +66,7 @@ def popen(
     env: Mapping[str, str] | None = None,
     silent: bool = False,
     stdout: int | IO[str] | None = None,
-    stderr: int | IO[str] = subprocess.STDOUT,
+    stderr: int | IO[str] | None = subprocess.STDOUT,
     interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
     terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
 ) -> tuple[int, str]:
diff --git a/nox/sessions.py b/nox/sessions.py
index df22f130..e0b4beb7 100644
--- a/nox/sessions.py
+++ b/nox/sessions.py
@@ -294,7 +294,7 @@ def run(
         log: bool = True,
         external: ExternalType | None = None,
         stdout: int | IO[str] | None = None,
-        stderr: int | IO[str] = subprocess.STDOUT,
+        stderr: int | IO[str] | None = subprocess.STDOUT,
         interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
         terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
     ) -> Any | None:
@@ -433,7 +433,7 @@ def run_install(
         log: bool = True,
         external: ExternalType | None = None,
         stdout: int | IO[str] | None = None,
-        stderr: int | IO[str] = subprocess.STDOUT,
+        stderr: int | IO[str] | None = subprocess.STDOUT,
         interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
         terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
     ) -> Any | None:
@@ -515,7 +515,7 @@ def run_always(
         log: bool = True,
         external: ExternalType | None = None,
         stdout: int | IO[str] | None = None,
-        stderr: int | IO[str] = subprocess.STDOUT,
+        stderr: int | IO[str] | None = subprocess.STDOUT,
         interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
         terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
     ) -> Any | None:
@@ -548,7 +548,7 @@ def _run(
         log: bool,
         external: ExternalType | None,
         stdout: int | IO[str] | None,
-        stderr: int | IO[str],
+        stderr: int | IO[str] | None,
         interrupt_timeout: float | None,
         terminate_timeout: float | None,
     ) -> Any:
@@ -611,7 +611,7 @@ def conda_install(
         success_codes: Iterable[int] | None = None,
         log: bool = True,
         stdout: int | IO[str] | None = None,
-        stderr: int | IO[str] = subprocess.STDOUT,
+        stderr: int | IO[str] | None = subprocess.STDOUT,
         interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
         terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
     ) -> None:
@@ -718,7 +718,7 @@ def install(
         log: bool = True,
         external: ExternalType | None = None,
         stdout: int | IO[str] | None = None,
-        stderr: int | IO[str] = subprocess.STDOUT,
+        stderr: int | IO[str] | None = subprocess.STDOUT,
         interrupt_timeout: float | None = DEFAULT_INTERRUPT_TIMEOUT,
         terminate_timeout: float | None = DEFAULT_TERMINATE_TIMEOUT,
     ) -> None: