O Jogo says United boss Ole Gunnar Solskjaer is looking for midfield reinforcements and wants the Portugal international's goalscoring threat.
Fernandes has a £90m release clause in his contract with the Portuguese side but United are trying to negotiate a lower fee in the coming days.
The Old Trafford club have already added £50million full-back Aaron Wan-Bissaka from Crystal Palace and Swansea's Daniel James for £17.5m this summer.
They will now hope they can push on with a huge deal for Fernandes, whose form saw him play a key role in his country's Nations League success.
He started as they beat Holland 1-0 in the inaugural final of the competition in June, and to date has 13 caps and one goal to his name.