Swansea City has confirmed the club has agreed transfer terms for winger.
The Premier League club has also agreed personal terms with 21 year old Daniel James, following a successful medical at Old Trafford.
The transfer is expected to be completed when FIFA’s international transfer window opens from June 11.
The club will make further comment once the transfer has been completed.
Ole Gunnar Solskjaer, the United manager, has said he wants to sign players with the right attitude who will "last here for many years", rather than looking to recruit "ready-made players".
And it appears, according to his former United team-mate Giggs, James fits right into his plans.
Giggs told Sky Sports News: "He is not only a fantastic player, but a fantastic guy as well.
"He's very level-headed and yes if it does go through, United have got a very talented and exciting player."
Asked what advice he had given to James ahead of the move, Giggs added: "Advice doesn't change. A club like that is interested in you for what you have been doing.
"Don't try and be anyone else, don't try and do anything different."
Meanwhile, Gareth Bale's future at Real Madrid is still up in the air. He does not appear to be in the plans of head coach Zinedine Zidane but a move away is made difficult for buying clubs due to his high wages.
Giggs, however, says he has seen no sign Bale is distracted by his complicated situation at the Bernabeu.
"I only see him in an environment where he is happy. He's with his mates. In Portugal, he trained really well and in his downtime he was really relaxed. He looks really good and I've been really pleased with him.
"He's dealt with so much in his career that he can handle most things. I've got no worries with Gareth."