The veteran is off contract at Old Trafford this summer, though could be offered a coaching role in the academy.
However, The Sun says Wrexham are eyeing Evans after their promotion to the Championship was confirmed last week.
Wrexham boss Phil Parkinson admits free agents from the Premier League will be on their shopping list.
He said: "We haven’t really spoken about anything. We’ve always got our eye on players who are free transfers and are going to be available.
“I think it’s interesting because the jump in salaries is incredible, mind-blowing. Even coming up to this level, the jump to get players of Championship quality is expensive.
“But obviously the next level, I don’t think people outside football quite realise.
"They think players in League One must be multi-millionaires, but the drop-off from what people read in the press about Premier League players is huge.