Portuguese media outlet A Bola, as quoted by Metro, is reporting that the Norwegian head coach is eager to bring the Benfica midfielder to Old Trafford.
The same article states that Solskjaer is eager for the 20-time English champions to get a deal over the line ahead of their bitter rivals Manchester City.
According to the same story, Liverpool FC and Tottenham Hotspur are also interested in the Portugal international after his impressive season.
The report goes on to suggest that the 24-year-old will command a transfer fee in the region of £85m in the summer transfer window.
Fernandes has scored an impressive 25 goals and has made 15 assists in 44 games in all competitions for the Portuguese club in the current campaign.
Manchester United are bound to be linked with a host of different players in the summer transfer window as Solskjaer looks to revamp the Red Devils squad.
The Red Devils are embroiled in a tight battle to secure a top-four finish and Champions League football next season.
Manchester United could find it difficult to sign the in-demand Portuguese midfielder if they don’t have Champions League football to offer next term.
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