United boss Ole Gunnar Solskjaer is a big fan of the midfielder, who scored an impressive 31 goals in 50 games last season.
The Norwegian sees Fernandes as key to strengthening his midfield and Starsport understands that the club are readying an offer.
Reports in Portugal have suggested the Red Devils are ready to launch a £56m bid for the Portugal playmaker.
But Sporting president Frederico Varandas says United will have to go significantly higher to land Fernandes.
“I don’t know if there are many or if there are few [interested clubs],” Varandas told RTP.
“What I know, a lot has been spoken of values, coming to the press, €55m, €62m… for that he doesn’t leave, for sure.
“If Bruno Fernandes leaves, players with quality will come. But if Bruno leaves.”
Fernandes and Newcastle youngster Sean Longstaff are United’s main midfield targets this summer.
Solskjaer needs to replace Ander Herrera after the tenacious midfielder left the club for free this summer.
The Reds also want to keep star man Paul Pogba despite interest from Real Madrid and Juventus.
Earlier this summer, Fernandes revealed that he had always ‘dreamed’ of playing in the Premier League fuelling rumours of an impending move to England.
“Obviously if an irrefutable proposal for me arrives, and it’s good for the club, let’s get together and decide together,” the Portuguese said.
“I always said that I was an ambitious player and from a very early age I have had a dream of playing in England, where you can live pure football without big controversy, without big cases.
“Now, any of the other leagues, Germany, Spain and Italy are also very good and ambitious.”
Recent reports suggested that Paris Saint-Germain have joined the race to sign Fernandes.
But Sporting’s valuation is putting the Ligue 1 champions off chancing their arm with a potential deal.