diff --git a/reframe/core/variables.py b/reframe/core/variables.py
index c8777503ce..e25fd7f484 100644
--- a/reframe/core/variables.py
+++ b/reframe/core/variables.py
@@ -39,9 +39,7 @@ class TestVar:
     :meta private:
     '''
 
-    __slots__ = (
-        'field', '_default_value', 'name', '__attrs__'
-    )
+    __slots__ = ('_field', '_default_value', '_name',)
 
     def __init__(self, *args, **kwargs):
         field_type = kwargs.pop('field', fields.TypedField)
@@ -53,8 +51,7 @@ def __init__(self, *args, **kwargs):
                 f'{fields.Field.__qualname__}'
             )
 
-        self.field = field_type(*args, **kwargs)
-        self.__attrs__ = dict()
+        self._field = field_type(*args, **kwargs)
 
     def is_defined(self):
         return self._default_value is not Undefined
@@ -73,35 +70,47 @@ def default_value(self):
         return copy.deepcopy(self._default_value)
 
     @property
-    def attrs(self):
-        # Variable attributes must also be returned by-value.
-        return copy.deepcopy(self.__attrs__)
+    def field(self):
+        return self._field
+
+    @property
+    def name(self):
+        return self._name
 
     def __set_name__(self, owner, name):
-        self.name = name
+        self._name = name
 
     def __setattr__(self, name, value):
         '''Set any additional variable attribute into __attrs__.'''
         if name in self.__slots__:
             super().__setattr__(name, value)
         else:
-            self.__attrs__[name] = value
+            setattr(self._default_value, name, value)
 
     def __getattr__(self, name):
-        '''Attribute lookup into __attrs__.'''
-        attrs = self.__getattribute__('__attrs__')
-        try:
-            return attrs[name]
-        except KeyError:
-            var_name = self.__getattribute__('name')
-            raise AttributeError(
-                f'variable {var_name!r} has no attribute {name!r}'
-            ) from None
+        '''Attribute lookup into the variable's value.'''
+        def_val = self.__getattribute__('_default_value')
+
+        # NOTE: This if below is necessary to avoid breaking the deepcopy
+        # of instances of this class. Without it, a deepcopy of instances of
+        # this class can return an instance of _UndefinedType when def_val
+        # is Undefined. This is because _UndefinedType implements a custom
+        # __deepcopy__ method.
+        if def_val is not Undefined:
+            try:
+                return getattr(def_val, name)
+            except AttributeError:
+                '''Raise the AttributeError below.'''
+
+        var_name = self.__getattribute__('_name')
+        raise AttributeError(
+            f'variable {var_name!r} has no attribute {name!r}'
+        ) from None
 
     def _check_is_defined(self):
         if not self.is_defined():
             raise ReframeSyntaxError(
-                f'variable {self.name} is not assigned a value'
+                f'variable {self._name} is not assigned a value'
             )
 
     def __repr__(self):
@@ -538,11 +547,6 @@ def inject(self, obj, cls):
             if var.is_defined():
                 setattr(obj, name, var.default_value)
 
-                # If the variable value itself has attributes, inject them.
-                value = getattr(obj, name)
-                for attr, attr_value in var.attrs.items():
-                    setattr(value, attr, attr_value)
-
             # Track the variables that have been injected.
             self._injected_vars.add(name)
 
diff --git a/unittests/test_variables.py b/unittests/test_variables.py
index fa86fdadad..6caf02a922 100644
--- a/unittests/test_variables.py
+++ b/unittests/test_variables.py
@@ -255,7 +255,12 @@ class MyTest(rfm.RegressionTest):
         v = variable(Foo, value=Foo())
         v.my_attr = 'Injected attribute'
 
+    class OtherTest(MyTest):
+        assert v.my_attr == 'Injected attribute'
+        v = Foo()
+
     assert MyTest().v.my_attr == 'Injected attribute'
+    assert not hasattr(OtherTest().v, 'my_attr')
 
 
 def test_local_varspace_is_empty():