diff --git a/monai/metrics/active_learning_metrics.py b/monai/metrics/active_learning_metrics.py
index 7a1654191e..4756e421d5 100644
--- a/monai/metrics/active_learning_metrics.py
+++ b/monai/metrics/active_learning_metrics.py
@@ -129,9 +129,7 @@ def compute_variance(
     y_pred = y_pred.float()
 
     if not include_background:
-        y = y_pred
-        # TODO If this utils is made to be optional for 'y' it would be nice
-        y_pred, y = ignore_background(y_pred=y_pred, y=y)
+        y_pred = ignore_background(y_pred=y_pred)
 
     # Set any values below 0 to threshold
     y_pred[y_pred <= 0] = threshold
diff --git a/monai/metrics/utils.py b/monai/metrics/utils.py
index a451b1a770..24817800a2 100644
--- a/monai/metrics/utils.py
+++ b/monai/metrics/utils.py
@@ -15,7 +15,7 @@
 from collections.abc import Iterable, Sequence
 from functools import cache, partial
 from types import ModuleType
-from typing import Any
+from typing import Any, overload
 
 import numpy as np
 import torch
@@ -51,21 +51,44 @@
 ]
 
 
-def ignore_background(y_pred: NdarrayTensor, y: NdarrayTensor) -> tuple[NdarrayTensor, NdarrayTensor]:
+@overload
+def ignore_background(y_pred: NdarrayTensor, y: None = ...) -> NdarrayTensor: ...
+
+
+@overload
+def ignore_background(y_pred: NdarrayTensor, y: NdarrayTensor) -> tuple[NdarrayTensor, NdarrayTensor]: ...
+
+
+def ignore_background(
+    y_pred: NdarrayTensor, y: NdarrayTensor | None = None
+) -> NdarrayTensor | tuple[NdarrayTensor, NdarrayTensor]:
     """
     This function is used to remove background (the first channel) for `y_pred` and `y`.
 
     Args:
         y_pred: predictions. As for classification tasks,
-            `y_pred` should has the shape [BN] where N is larger than 1. As for segmentation tasks,
+            `y_pred` should have the shape [BN] where N is larger than 1. As for segmentation tasks,
             the shape should be [BNHW] or [BNHWD].
-        y: ground truth, the first dim is batch.
+        y: ground truth, the first dim is batch. (Optional)
 
+    Returns:
+        NdarrayTensor | tuple[NdarrayTensor, NdarrayTensor]:
+        - If `y` is None: returns background-removed `y_pred` only.
+        - If `y` is provided: returns a tuple of (background-removed `y_pred`, background-removed `y`).
     """
 
-    y = y[:, 1:] if y.shape[1] > 1 else y  # type: ignore[assignment]
-    y_pred = y_pred[:, 1:] if y_pred.shape[1] > 1 else y_pred  # type: ignore[assignment]
-    return y_pred, y
+    y_pred_out = y_pred
+    if y_pred.shape[1] > 1:
+        y_pred_out = y_pred[:, 1:]  # type: ignore
+
+    if y is None:
+        return y_pred_out
+
+    y_out = y
+    if y.shape[1] > 1:
+        y_out = y[:, 1:]  # type: ignore
+
+    return y_pred_out, y_out
 
 
 def do_metric_reduction(