Fernandes, 24, is hot property this summer after being involved in 50 goals for Sporting Lisbon in the 2018/19 season.
Sporting Lisbon are prepared to cash in on Fernandes, but are so far refusing to budge on their £70million asking price.
Solskjaer has identified Fernandes as one of two midfielders he wants to sign this summer, but Correio da Manha claim the United boss’ wishes is at odds with the club board.
United have indicated they would be willing to pay £50m for Fernandes, but are reluctant to offer more for the attacker.
The board are concerned about paying a massive fee for a player who does not play regularly in the Champions League.
United failed to qualify for next season’s Champions League, though, the club are determined to back Solskjaer in the transfer market.
Solskjaer wants to build his side around young, British talent and has signed Daniel James and Aaron Wan-Bissaka as part of that vision.
Newcastle midfielder Sean Longstaff is the second midfield target for Solskjaer, with United in danger of losing Paul Pogba.
The Frenchman wants to leave Old Trafford this summer and is being linked with a switch to Real Madrid and a return to Juventus.
United’s board will not sanction an improved bid for Fernandes unless Pogba leaves.
Pogba’s agent, Mino Raiola, has made repeated statements about Pogba’s desire to exit United, but the World Cup winner joined up with the Red Devils pre-season squad and played against Perth Glory over the weekend.
After a 2-0 win over Perth Glory, Pogba dodged speculation about his future, replying to questions in the mixed zone: ‘There’s no need – who needs to talk?’