Ole Gunnar Solskjaer wants to make 21-year-old his first summer signing as he looks to overhaul his squad.
But Swansea are ready to drive up the price with a number of clubs interested in James, according to the Mirror.
United were reportedly ready to pay £15million for the Welshman but that price could now be inflated.
That’s because the liked of Newcastle, Everton and Leeds are all monitoring James and may be tempted into bidding.
Swansea are aware they need to cash in on their starlet this summer as he has just one year left remaining on his contract.
The report claims United have yet to make a formal offer for the midfielder despite their interest.
Leeds very nearly signed James in January only for Swansea to pull the plug on the deal on deadline day.
And they could renew their interest if they are promoted to the Premier League.
Wales boss and Manchester United hero Ryan Giggs was full of praise for James earlier this season.
“He’s a talent,” he said back in March.
“When you’ve got that raw pace, you’re a threat at any level so as a winger, obviously for me playing as a winger, when I was younger, you then have to develop the other parts of your game which I feel he is doing.
“He’s played up front as well which will help him because that gives you an appreciation of what you need to do.”
United finished their Premier League campaign with a humiliating 2-0 loss to Cardiff at Old Trafford.
That meant the Red Devils finished down in sixth place, a massive 32 points behind champions Manchester City.
As a result United will be playing Europa League football next season.
Solskjaer is expected to be very busy this summer as he looks to overhaul his squad and bring in new players.
A number of stars could leave Old Trafford as well with the Norwegian set to be ruthless.