United have identified Fernandes and Longstaff as targets after securing the services of two signings this summer so far.
The Red Devils have snatched up Daniel James and Aaron Wan-Bissaka this summer and there are also plans afoot to sign Harry Maguire.
After an abysmal year, Solskjaer is desperate to take his former club back to the top and wants young, British talents to bolster his squad.
The Old Trafford outfit finished sixth in the Premier League amid a multitude of problems on and off the pitch.
Losing Ander Herrera was a big blow to Solskjaer’s squad, who are now looking light in midfield.
With Nemanja Matic and Paul Pogba’s futures up in the air, the former Cardiff manager is desperate to bolster his ranks.
They are looking at both Longstaff and Fernandes, but the Telegraph report it is the former that they are pursuing more aggressively.
The Newcastle midfielder impressed in his limited game-time last year before injury ended his season.
But the Red Devils have been stunned by the Toon’s £50m valuation of the 21-year-old – who has made just nine Premier League appearances.
Solskjaer is keen on the starlet so executive vice-chairman Ed Woodward will continue negotiations.
He is hoping that the price can be dropped and will test Newcastle’s resolve with a bid.
Meanwhile, Fernandes remains on the radar but Sporting are demanding £70m for the 24-year-old.
The Portuguese ace had a brilliant year last season, scoring 32 and assisting 18.
But as of yet, there has not been any concrete progress on any kind of transfer – though the player himself has admitted he wants to ply his trade in England.
He said: “I told you I’d like to play in England, but that’s not what interests me. It may be when the club decides.”