diff --git a/cosmos/airflow/graph.py b/cosmos/airflow/graph.py
index 209a6d9614..71bff501fc 100644
--- a/cosmos/airflow/graph.py
+++ b/cosmos/airflow/graph.py
@@ -241,6 +241,7 @@ def create_task_metadata(
     source_rendering_behavior: SourceRenderingBehavior = SourceRenderingBehavior.NONE,
     normalize_task_id: Callable[..., Any] | None = None,
     test_behavior: TestBehavior = TestBehavior.AFTER_ALL,
+    test_indirect_selection: TestIndirectSelection = TestIndirectSelection.EAGER,
     on_warning_callback: Callable[..., Any] | None = None,
     detached_from_parent: dict[str, DbtNode] | None = None,
 ) -> TaskMetadata | None:
@@ -271,6 +272,8 @@ def create_task_metadata(
         }
 
         if test_behavior == TestBehavior.BUILD and node.resource_type in SUPPORTED_BUILD_RESOURCES:
+            if test_indirect_selection != TestIndirectSelection.EAGER:
+                args["indirect_selection"] = test_indirect_selection.value
             args["on_warning_callback"] = on_warning_callback
             exclude_detached_tests_if_needed(node, args, detached_from_parent)
             task_id, args = _get_task_id_and_args(
@@ -367,6 +370,7 @@ def generate_task_or_group(
         source_rendering_behavior=source_rendering_behavior,
         normalize_task_id=normalize_task_id,
         test_behavior=test_behavior,
+        test_indirect_selection=test_indirect_selection,
         on_warning_callback=on_warning_callback,
         detached_from_parent=detached_from_parent,
     )
diff --git a/tests/airflow/test_graph.py b/tests/airflow/test_graph.py
index 728b86283b..1cc2418966 100644
--- a/tests/airflow/test_graph.py
+++ b/tests/airflow/test_graph.py
@@ -808,6 +808,43 @@ def test_create_task_metadata_normalize_task_id(
         assert "task_display_name" not in metadata.arguments
 
 
+@pytest.mark.integration
+def test_build_airflow_graph_with_build_and_buildable_indirect_selection():
+    with DAG("test-build-buildable", start_date=datetime(2022, 1, 1)) as dag:
+        task_args = {
+            "project_dir": SAMPLE_PROJ_PATH,
+            "conn_id": "fake_conn",
+            "profile_config": ProfileConfig(
+                profile_name="default",
+                target_name="default",
+                profile_mapping=PostgresUserPasswordProfileMapping(
+                    conn_id="fake_conn",
+                    profile_args={"schema": "public"},
+                ),
+            ),
+        }
+        render_config = RenderConfig(
+            test_behavior=TestBehavior.BUILD,
+        )
+        build_airflow_graph(
+            nodes=sample_nodes,
+            dag=dag,
+            execution_mode=ExecutionMode.LOCAL,
+            test_indirect_selection=TestIndirectSelection.BUILDABLE,
+            task_args=task_args,
+            dbt_project_name="astro_shop",
+            render_config=render_config,
+        )
+
+    topological_sort = [task.task_id for task in dag.topological_sort()]
+    expected_sort = ["seed_parent_seed_build", "parent_model_build", "child_model_build", "child2_v2_model_build"]
+    assert topological_sort == expected_sort
+
+    for task in dag.tasks:
+        if hasattr(task, "indirect_selection"):
+            assert task.indirect_selection == TestIndirectSelection.BUILDABLE.value
+
+
 @pytest.mark.parametrize(
     "node_type,node_unique_id,test_indirect_selection,additional_arguments",
     [