diff --git a/pylint/checkers/refactoring/refactoring_checker.py b/pylint/checkers/refactoring/refactoring_checker.py
index f87e9f60e1..674ebe19ab 100644
--- a/pylint/checkers/refactoring/refactoring_checker.py
+++ b/pylint/checkers/refactoring/refactoring_checker.py
@@ -21,7 +21,7 @@
 from pylint import checkers
 from pylint.checkers import utils
 from pylint.checkers.utils import node_frame_class
-from pylint.interfaces import Confidence, HIGH, INFERENCE
+from pylint.interfaces import HIGH, INFERENCE, Confidence
 
 if TYPE_CHECKING:
     from pylint.lint import PyLinter
@@ -2281,7 +2281,7 @@ def _enumerate_with_start(
     def _get_start_value(self, node: nodes.NodeNG) -> tuple[int | None, Confidence]:
         confidence = HIGH
 
-        if isinstance(node, nodes.Name):
+        if isinstance(node, (nodes.Name, nodes.Call)):
             inferred = utils.safe_infer(node)
             start_val = inferred.value if inferred else None
             confidence = INFERENCE
diff --git a/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py b/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
index fbf0597255..e5cb135148 100644
--- a/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
+++ b/tests/functional/u/unnecessary/unnecessary_list_index_lookup.py
@@ -120,3 +120,13 @@ def process_list_again(data):
 
 for idx, val in enumerate(series, START):
     print(series[idx])  # [unnecessary-list-index-lookup]
+
+START = [1, 2, 3]
+for i, k in enumerate(series, len(START)):
+    print(series[idx])
+
+def return_start(start):
+    return start
+
+for i, k in enumerate(series, return_start(20)):
+    print(series[idx])