The Red Devils are still in pursuit of Borussia Dortmund and England winger Jadon Sancho and Solskjaer wants to sell James to fund the move.
Dortmund are holding out for a fee of around £108m for Sancho and United are struggling to meet the enormous asking price.
The Norwegian is happy to let James leave on a permanent basis for around £25m, if that means he can secure the Sancho signing before Monday night’s transfer deadline.
However, the board at Old Trafford are not so sure on this move, with ESPN reporting that the manager needs to convince them that James is surplus to requirements.
James arrived at Old Trafford in the summer of 2019 with United paying Swansea £15m for the winger.
He enjoyed an impressive start to life as a Manchester United player, but his form tailed off and he found himself out of the team by the end of last season, with Mason Greenwood taking his place on the right wing.
James was a surprise starter in the first Premier League match of this season for Manchester United, but was substituted for Greenwood at half-time against Crystal Palace and did not get on the pitch against Brighton in the second league game of the campaign.
Solskjaer wants to upgrade the 22-year-old with Sancho the key target, but Barcelona’s Ousmane Dembele and Sevilla’s Lucas Ocampos also options if they cannot find the cash for the Englishman.