Mourinho continued his impressive run against Arsene Wenger - which now sees him unbeaten in nine games against the Frenchman - after Chelsea swaggered to a 2-0 victory over the Gunners in the fourth round of the Capital One Cup.
Ozil, who signed for Arsenal in a £42.5million deal during the closing hours of the transfer window and came on as a second-half substitute in his side's defeat, played under Mourinho at Real Madrid.
Getting shirt: Mesut Ozil gives his Arsenal top to Chelsea manager Jose Mourinho after the game
And it appears the Germany international still shares a special bond with the self-proclaimed Special One after handing the Portuguese his strip following the final whistle.
Ozil replaced Ryo Miyaichi after an hour at the Emirates, but had little effect on the League Cup clash as Chelsea cruised to victory.