The Red Devils have been heavily linked with a January raid on Emirates Stadium for a creative talent who continues to run down his current contract.
Wilkins, though, doubts that Ozil will end up at Old Trafford as questions will be asked of his “work ethic”.
Instead, the former United and Chelsea midfielder believes that Mourinho could be tempted to make an approach for a Brazilian forward he has previously worked with at Stamford Bridge.
Wilkins told Sporting Bet: "I would have sold Ozil in the summer, the same with [Alexis] Sanchez – it's embarrassing. I find it quite sad that the club have allowed [Arsene] Wenger to take the stance of not selling them, potentially costing the club £120 million in fees that they're now not getting.
"Mesut Ozil won't go to Old Trafford because he doesn't have the work ethic that Mourinho looks for in his players. I actually see Willian as being the likely player to head to Old Trafford. Jose is an enormous admirer of Willian and he would be a special signing for United, but I pray that Chelsea don't let him go.
"Ozil needs to go back to Germany, enjoy his football again and get around the pitch as he likes doing. In the Premier League, you're expected to work hard defensively for your team, and I don't think Mesut does that enough. Against Spurs, he was excellent in doing that, tracking Christian Eriksen, but he needs to do that every game, it can't be one game in 20."
While questioning how much interest United actually hold in Ozil, Wilkins is also refusing to read too much into reporters suggesting that David Luiz could be offered a path to Manchester.
The Brazil international has clashed with Chelsea boss Antonio Conte at times this season, but he is another performer who is considered to be wrong for Mourinho’s system at Old Trafford.
He added: “As far as I’m concerned, David Luiz can go to United tomorrow as a centre-half. If he goes as a holding midfielder, I wouldn’t let him leave. David Luiz, as a centre-half, does not fit the requirements of a top-level football club – he makes far too many errors.
“I don’t think Jose Mourinho will have David. He wants to keep clean sheets and beat opposition one or two nil and with Luiz, he will struggle to do that.”
Luiz has not figured in a Premier League game for Chelsea since October 28, although he is currently sidelined with a niggling knee complaint.