The 22-year-old was a key player for his Portuguese club during the 2021-22 campaign, making 47 appearances in all competitions, contributing four goals and five assists in the process.
Vitinha only has little over two years left to run on his current deal, though, and there is believed to be a €40m (£34.8m) release clause in his contract, which has led to a host of speculation surrounding his future.
Liverpool, Bayern Munich, Lazio and Real Madrid are among the clubs to be credited with an interest in the Portugal international over the last few weeks.
However, according to Record, Man United are leading the race for the midfielder, with the English club's new head coach Erik ten Hag a huge admirer of his talents.
The report claims that Ten Hag believes that Vitinha's style is perfect for his brand of football, and the midfielder's exit from Porto 'is getting closer'.
Vitinha, who is on the books of well-known agent Jorge Mendes, represented Wolverhampton Wanderers on loan during the 2020-21 campaign, making 22 appearances, scoring once and providing one assist.
Wolves had the opportunity to sign the Portuguese on a permanent basis for £17m in the summer of 2021 but did not exercise the option due to the financial issues caused by the coronavirus pandemic.
The midfielder scored twice and registered four assists in 30 league appearances during the 2021-22 campaign, as Porto finished six points ahead of second-place Sporting Lisbon to win the title.
He also played seven times in the Taca de Portugal, contributing two goals and one assist, in addition to making 10 European appearances, six in the Champions League and four in the Europa League.
Vitinha showed his versatility in the latter stages of last season by operating as a left-sided midfielder, but he largely featured as a central midfielder for the Blue and Whites in 2021-22.
The playmaker has also recently worked his way into the Portuguese national side, featuring in their last two UEFA Nations League fixtures against Czech Republic and Switzerland.
Man United remain in discussions with Barcelona over a deal for Frenkie de Jong, with the Netherlands international viewed as the club's leading summer transfer target.
However, two new midfielders could potentially arrive at Old Trafford in the current market, as both Nemanja Matic and Paul Pogba are leaving this summer on free transfers.
Man United have also allegedly offered a contract to Christian Eriksen, with the Denmark international said to have made the decision to leave Brentford on a free transfer this summer.