James has emerged as one of the outstanding young talents in the UK this season, scoring four goals and assisting eight for the Swans.
The winger earned his first senior international cap last November, before scoring the winner in Wales’ 1-0 Euro 2020 qualifier win over Slovakia in March.
There are a host of Premier League clubs circling for his signature, but Manchester United are expected to have their papers signed.
The 21-year-old has just one year left on his contract in south Wales and is valued at £10million.
United have been watching James to see his comfortability on the right wing, where they want to strengthen.
Swansea left James out of the squad for their final-day clash with Blackburn to avoid a potential injury which could scupper a summer transfer.
James looked set for a switch to Leeds in January but Swansea pulled out in the final stages.
Man Utd transfer news: Daniel James is expected to join the Red Devils this summer
Man Utd transfer news: Daniel James did not play on the final day to avoid injury
As it stands, Solskjaer will have the final say on transfers at United.
The club are looking to bring in a director of football, however, who will liaise with Solskjaer on signings and coordinate recruitment.
Ahead of United’s 1-1 draw with Huddersfield last weekend, Solskjaer sent a message to those currently in the squad.
“You give people a chance but, sometimes, you’ve got to be ruthless and say: ‘Sorry but you had your chance,’” Solskjaer said.
Man Utd transfer news: Ole Gunnar Solskjaer will have free rein on transfers as it stands
“I’m not afraid to do that. You say that ‘dream’ for some of them – if you show me that it’s your dream I don’t think I’ll be showing them the door.
“That’s the thing because they’re talented enough. You have to perform at Man Utd, and to perform you’ve got to really work towards that dream, and that’s what we’re doing every day as a staff.
“You want to see [the players saying]: ‘This is my dream, I’m going to do whatever it takes,’ because that’s probably what they started off [thinking] when they were young kids.
“They want to play at big clubs, they want to win trophies, and when you have that desire, drive inside yourself, you’ll be successful at a club like this.”