According to the Mirror's John Richardson, United boss Jose Mourinho wants to undo what he believes was a "huge mistake" on the part of his predecessor, Louis van Gaal, who sold Evans to West Brom for £6 million in the summer of 2015.
The Red Devils face the prospect of having to cope without Eric Bailly for three months because of surgery on his ankle, so they are said to be ready to join Arsenal and Manchester City in the pursuit of Evans, though the Baggies are believed to want around £30 million for their captain.
BBC Sport's Simon Stone believes Bailly will be missed at Old Trafford:
The Ivorian has established himself as United's top centre-back since he arrived at the club last year, and his absence will do the team no favours despite the form of some of their other defenders in recent weeks.
Samuel Luckhurst of the Manchester Evening News recently praised Victor Lindelof, who has impressed of late after a difficult start to his career at Old Trafford, while football writer Liam Canning has been pleased with Phil Jones' contributions this year:
However, Canning also noted the Red Devils' reliance on goalkeeper David De Gea to dig them out of trouble:
That's where Evans could come in. The 29-year-old, who made 198 appearances for United before his departure for West Brom, has shown himself to be one of the Premier League's most reliable defenders during his time at the Hawthorns, resulting in the likes of Arsenal and City's interest in him.
The Northern Ireland international may not be a particularly long-term solution for any of the interested sides given he turns 30 in January, and he would not be a marquee capture, either.
However, he could still have a lot to offer in the coming years as an experienced and consistently strong option at the back.