The Serbia international has seen his opportunities restricted under Ole Gunnar Solskjaer this season, making just six Premier League appearances since August.
Moreover, the midfielder's current contract expires in June, meaning that he could leave for free over the summer.
According to The Sun, Chicago are prepared to do a deal for Matic in this window, offering the player a salary of £5m a year.
Meanwhile, United are focusing on adding a midfielder to their roster in the form of Sporting Lisbon star Bruno Fernandes, with the two clubs said to be in advanced talks. body check tags ::