The Sun says the ex-England defender is not in any of United's plans this season, after being left out of their Champions League squad.
The 28-year-old has not played a single minute so far this season, and made just two Premier League appearances last year.
Now he wants to leave and kick-start his career elsewhere in England.
A number of Premier League clubs have shown interest in him in the past, and Fulham looked at him this summer.
United only extended his contract last year until 2023 – keeping him on a deal worth nearly £100,000-a-week before bonuses.
But manager Ole Gunnar Solskjaer has no plans to use Jones much this campaign, with just fleeting appearances in the FA and EFL Cup planned.