United have already snapped up Aaron Wan-Bissaka and Daniel James this summer.
But both stars are relatively inexperienced and Ole Gunnar Solskjaer wants more established players in his ranks.
Fernandes, 24, could fit the bill.
The midfielder has been an ever-present at Sporting for the last two seasons and has racked up over 100 appearances.
“Man Utd are closing in on Bruno Fernandes ”
The Portugal international also spent four season in Serie A with Sampdoria and Udinese respectively.
Journalist Nico Schira, who works for Italian newspaper Gazzetta dello Sport, reckons a deal is on the cards although his valuation remains a sticking point.
It’s claimed Manchester United have tabled a £55m bid, but Sporting are holding out for at least £62m.
Solskjaer is also pushing to get a deal for Leicester defender Harry Maguire sealed.
Starsport understand a deal is close despite Manchester City’s early attempts to derail the move.
“We’re still in the market looking to do some business, as I’ve said before,” the United manager said earlier this month.
“But we’re patient, we’re Manchester United, we don’t have to sell and don’t have to overpay either. You have to have the right players at the right price.
“And if you look at the squad we’ve got now, there are so many good players anyway.
“I’m sure with a good pre-season behind us – that’s the main thing now – the ones who are here are working hard want to improve.
“It’s not just about fitness work, it’s about robustness, this squad needs to be more robust when the season gets going.
“Last year, we had a run of I don’t know how many games without any defeats but the end was disappointing because we couldn’t get back to winning ways and need to get back to that.
“Doing business in the football market is not going to be a quick fix overnight. And we have players here who I trust.
“There are fantastic players here, loads of players I know are gonna be successful at this club and we’ve signed two in Dan and Aaron, with their speed and hunger, with quality that will be part of that.
“And I’m coaching and managing them here, the business side of it is you have to be in the market and, as I said, we don’t have any offers for our players.”