The 21-year-old looks set to leave the Liberty Stadium this summer after an impressive campaign in the Championship and with just one year left on his deal and no extension in sight.
The Mirror believes that the Swans want to use interest from United as a way of starting a bidding war between top flight clubs, with Everton, Newcastle United and promotion hopefuls Leeds United showing interest.
Swansea have set a starting price of £15 million but are hopeful that a bigger offer will arrive, according to the report.
The Wales international almost joined Leeds on deadline day during the January transfer window and the Elland Road club are still keen on securing his signature, particularly if they achieve promotion through the play-offs.
However, James is on United’s shortlist of summer targets as Ole Gunnar Solskjaer plans a summer rebuild at Old Trafford after a disappointing campaign that saw them finish sixth in the Premier League.
James, who doesn’t turn 22 until November, scored four goals and provided nine assists in 33 Championship appearances this season.
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