The 27-year-old has been a constant performer for Juventus and new United manager David Moyes is a known admirer of the Italian international.
And though Marchisio currently wants to bring more success to the Serie A champions, he refused to commit his long term future to the club.
"For the past seven years, my name has always come up when the transfer market was discussed," he told Tuttosport.
"Then again, you never know what will happen in football. I would not be the first player to leave his boyhood club."
Marchisio made 39 appearances scoring eight times in all competitions as he helped Juventus win the Serie A title and reach the quarter-finals of the Champions League before succumbing to eventual winners Bayern Munich.