United are reportedly keen to make a splash in the transfer window, with claims being made that the side have a budget of around £150M to spend on midfield targets.
With Casemiro set to leave once the season is over and Manuel Ugarte rumoured to be departing, the Red Devils will need a number of new faces in the middle of the park especially now they have qualified for the Champions League.
Several midfielders have been linked with United in recent weeks, including the likes of Sandro Tonali, former Newcastle midfielder Elliot Anderson, Adam Wharton, Aurelien Tchouameni and Carlos Baleba.
However, speaking on The Good, The Bad and The Football podcast, Schmeichel suggested that United make a move for a former Arsenal star.
“I think we should go and sign Xhaka. I make my case, what we are going to do is build the team around Kobbie, right. Now Casemiro is leaving. Now you bring in somebody like (Adam) Wharton, (Elliot) Anderson whatever… that’s still young, that’s still untried.
“What we need and what we don’t really have apart from Harry (Maguire) and Bruno (Fernandes) in that team is proper leadership.”
"When I look at what Xhaka’s done for Sunderland, Xhaka is the reason they are where they are," Schmeichel added. "He has been absolutely amazing, his leadership qualities are great, he can play 80 per cent of the games, he’s a really good player. We’re desperate for more leadership."
Xhaka still has two more years to run on the three-year deal he signed when he joined from Bayer Leverkusen. However, a call from United could entice him to leave.