The Uruguay international joined the Nerazzurri last summer on a free transfer after a successful spell at Atletico Madrid.
But he has struggled to settle in Italy and has faced a tough fight with youngster Alessandro Bastoni for a place in Antonio Conte’s starting line-up.
With Jan Vertonghen’s contract set to expire at the end of the season, Mourinho wants to add experience and leadership to a backline that has failed to impress this term.
But he is likely to face competition from his former employers United, who are also in the hunt for an experienced centre-back.
Additionally, Valencia could offer Godin a route back to Spain and La Liga.
The defender won the La Liga title, the Copa del Rey, two Europa League titles and reached two Champions League finals during his nine-year spell with Atleti.
This term, he has made 17 league appearances for Inter, who were in third place in the Serie A table before Italian football was suspended amid the coronavirus outbreak.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.