The defender left United for the Hawthorns in 2015 when Louis van Gaal sanctioned a £6m move to West Brom.
Evans excelled during his first two seasons in the Midlands and the Baggies turned down bids from Arsenal and Manchester City for the Northern Ireland international in 2017.
However, West Broms form plummetted during Evans third season at the club and they are now all but relegated to the Championship after a disappointing campaign.
West Brom had valued Evans at around £25m but a clause in his contract means he can leave the club for £3m if the Baggies are relegated.
Mourinhos side have the second best defence in the league this term but he wants to strengthen and views Evans as the perfect choice, according to the Sun.
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The Special One is happy with his attack and believes they will benefit from a lack of arrivals this summer.
However, he wants to strengthen in full-back areas and Evans arrival would put Marcos Rojo and Victor Lindelof, who arrived just last summer, at risk.