The Argentine attacker has voiced his opinion that the caretaker boss deserves the position on a permanent basis following the side's good results in recent weeks
Inter have lost only once in eight games under Stramaccioni, and still have a chance to qualify for the Champions League after Sunday's 4-2 derby win over AC Milan, and Milito is hopeful that he will remain in charge beyond the current season.
"I think he deserves the job, and we all hope that he will stay. We have already said many times that we are very happy with him," Milito said to Sky.
"It's obviously up to the club to make a decision about this, but I hope that he stays. He is a great coach, who is still young and has a lot of desire. Things are going very well under him."
Despite Milito's preference for Stramaccioni, Inter have been linked with coaches such as Laurent Blanc, Cesare Prandelli and Andre Villas-Boas in the past few weeks.