diff --git a/transformations/tests/test_data_offload.py b/transformations/tests/test_data_offload.py
index 4b60148fb..8745a2bf5 100644
--- a/transformations/tests/test_data_offload.py
+++ b/transformations/tests/test_data_offload.py
@@ -388,24 +388,20 @@ def test_global_variable_analysis(frontend, key, config, global_variable_analysi
         nval_dim = '1:5'
         nfld_data = set()
         nval_data = set()
-        nval_offload = set()
-        nfld_offload = set()
     else:
         nfld_dim = 'nfld'
         nval_dim = 'nval'
         nfld_data = {('nfld', 'global_var_analysis_header_mod')}
         nval_data = {('nval', 'global_var_analysis_header_mod')}
-        nval_offload = {'nval'}
-        nfld_offload = {'nfld'}
 
     expected_trafo_data = {
         'global_var_analysis_header_mod': {
             'declares': {f'iarr({nfld_dim})', f'rarr({nval_dim}, {nfld_dim})'},
-            'offload': {f'iarr({nfld_dim})', f'rarr({nval_dim}, {nfld_dim})'} | nval_offload | nfld_offload,
+            'offload': {}
         },
         'global_var_analysis_data_mod': {
             'declares': {'rdata(:, :, :)', 'tt'},
-            'offload': {'rdata(:, :, :)', 'tt', 'tt%vals'}
+            'offload': {}
         },
         'global_var_analysis_data_mod#some_routine': {'defines_symbols': set(), 'uses_symbols': set()},
         'global_var_analysis_kernel_mod#kernel_a': {
@@ -454,6 +450,14 @@ def test_global_variable_offload(frontend, key, config, global_variable_analysis
         'driver': {'role': 'driver'}
     }
 
+    # OMNI handles array indices and parameters differently
+    if frontend == OMNI:
+        nfld_dim = '1:3'
+        nval_dim = '1:5'
+    else:
+        nfld_dim = 'nfld'
+        nval_dim = 'nval'
+
     scheduler = Scheduler(
         paths=(global_variable_analysis_code,), config=config, seed_routines='driver',
         frontend=frontend, xmods=(global_variable_analysis_code,)
@@ -462,6 +466,30 @@ def test_global_variable_offload(frontend, key, config, global_variable_analysis
     scheduler.process(GlobalVarOffloadTransformation(key=key))
     driver = scheduler['#driver'].ir
 
+    if key is None:
+        key = GlobalVariableAnalysis._key
+
+    expected_trafo_data = {
+        'global_var_analysis_header_mod': {
+            'declares': {f'iarr({nfld_dim})', f'rarr({nval_dim}, {nfld_dim})'},
+            'offload': {f'iarr({nfld_dim})', f'rarr({nval_dim}, {nfld_dim})'}
+        },
+        'global_var_analysis_data_mod': {
+            'declares': {'rdata(:, :, :)', 'tt'},
+            'offload': {'rdata(:, :, :)', 'tt', 'tt%vals'}
+        },
+    }
+
+    # Verify module offload sets
+    for item in [scheduler['global_var_analysis_header_mod'], scheduler['global_var_analysis_data_mod']]:
+        for trafo_data_key, trafo_data_value in item.trafo_data[key].items():
+            assert (
+                sorted(
+                    tuple(str(vv) for vv in v) if isinstance(v, tuple) else str(v)
+                    for v in trafo_data_value
+                ) == sorted(expected_trafo_data[item.name][trafo_data_key])
+            )
+
     # Verify imports have been added to the driver
     expected_imports = {
         'global_var_analysis_header_mod': {'iarr', 'rarr'},
diff --git a/transformations/transformations/data_offload.py b/transformations/transformations/data_offload.py
index cfc28e54f..dae7d3326 100644
--- a/transformations/transformations/data_offload.py
+++ b/transformations/transformations/data_offload.py
@@ -323,17 +323,6 @@ def _map_var_to_module(var):
                 _map_var_to_module(var) for var in defines_imported_symbols
             }
 
-        # Propagate offload requirement to the items of the global variables
-        successors_map = CaseInsensitiveDict(
-            (item.name, item) for item in successors if isinstance(item, ModuleItem)
-        )
-        for var, module in chain(
-            item.trafo_data[self._key]['uses_symbols'],
-            item.trafo_data[self._key]['defines_symbols']
-        ):
-            if successor := successors_map.get(module):
-                successor.trafo_data[self._key]['offload'].add(var)
-
         # Amend analysis data with data from successors
         # Note: This is a temporary workaround for the incomplete list of successor items
         # provided by the current scheduler implementation
@@ -476,9 +465,28 @@ def transform_subroutine(self, routine, **kwargs):
         """
         role = kwargs.get('role')
         successors = kwargs.get('successors', ())
+        item = kwargs['item']
 
         if role == 'driver':
             self.process_driver(routine, successors)
+        elif role == 'kernel':
+            self.process_kernel(item, successors)
+
+    def process_kernel(self, item, successors):
+        """
+        Propagate offload requirement to the items of the global variables
+        """
+        successors_map = CaseInsensitiveDict(
+            (item.name, item) for item in successors if isinstance(item, ModuleItem)
+        )
+        for var, module in chain(
+            item.trafo_data[self._key]['uses_symbols'],
+            item.trafo_data[self._key]['defines_symbols']
+        ):
+            if var.type.parameter:
+                continue
+            if successor := successors_map.get(module):
+                successor.trafo_data[self._key]['offload'].add(var)
 
     def process_driver(self, routine, successors):
         """