The 32-year-old is currently on a season-long loan at Milan from Chelsea after a disappointing spell in West London.
Shevchenko has struggled to establish himself in Carlo Ancelotti's plans this season, but he is keen to stay with the Rossoneri.
"The truth is that I may not be given the chance to stay at Milan," Shevchenko told Gazzetta dello Sport.
"I know that it has been a difficult season, but I would love to stay put.
"I will keep trying as hard as I can to prove that I can still do good things for this club.
"At least I am getting a chance to play some games now and that makes everything easier.
"It has been disappointing not to get more playing time, but that's just the way it is at a club like Milan."