The Portugal international has taken the Premier League by storm since joining from Sporting back in January, scoring 10 goals and assisting a further eight in only 17 appearances.
Although the 26-year-old seem to had have a close relationship with Ole Gunnar Solskjaer since his move to Old Trafford was confirmed - an apparent disagreement has threatened to cause a divide.
The news that the two big La Liga sides are plotting a potential offer comes after Fernandes admitted he wasn’t totally satisfied with a decision made by his manager during their last outing.
The Sun have reported that both Barcelona and Real Madrid are monitoring the situation of Fernandes.
"There's been a lot of speculation about that," Fernandes is quoted as saying by A Bola in relation to reports that he has had disagreements during his time at United.
"First it was a discussion with team-mates, as it did not stick, it was a discussion with only one team-mate [Victor Lindelof], as it did not stick now, it is the discussion with Solskjaer.
"I believe it is a way to destabilise the group. What was said is in no way true.”
"I was replaced at half-time, it is true, by technical option.
"The coach told me that the game was almost over and that we would have a lot of games ahead of us.
"I was not satisfied but said nothing that could harm the group."
Before adding: ”Do not use my name, my colleagues or the coach to make trouble at Manchester United.
"The atmosphere is good and the team is ready to give an answer in the next game.
Solskjaer said when asked about the apparent discontent of his midfielder this week: “There are many reasons behind subs in a game and if I explain every time I take a player off, I don’t think that’s right.
“I explained to Bruno and he accepted it, no problem.”