The midfielder, still only 22, spent last season on loan at Verona and has been offered to a host of clubs, including United.
Slavisa Jokanović, the United boss, knows that midfield is an area of his squad that will need attention this summer, with Sander Berge expected to follow John Lundstram out of the Bramall Lane exit door.
But who is Vieira, what’s his background and would a move suit all parties?
Born in Guinea-Bissau in July 1998, Vieira moved with his family to England in 2011. He and his twin brother, Romario, are both named after former top strikers and after moving to Yorkshire from the north-east, Ronaldo signed for the York-based i2i Football Academy.
From there he was spotted by Leeds United, signing a professional deal in 2016. Romario joined his brother at Elland Road the same year.
Vieira was expected to primarily play for Leeds’ development squad after signing, but he made 38 appearances for the first team in his breakthrough campaign under Garry Monk after making his senior debut at 17.
“I got involved way more than I thought I would,” Vieira said at the time. “I thought I was maybe going to train with the first team a few times and then play 23s football but that didn’t happen at all.”
In 2018 he was named 20th in a list of the most promising under-20 players across the whole of Europe, alongside the likes of Gianluigi Donnarumma and Kylian Mbappe, and was sold to Sampdoria for around £6million in 2018.
Vieira qualified to play for England because of the amount of time he had spent in the country and after discussions with his family, and despite initially admitting he was leaning towards representing Portugal, he chose the three lions.
In 2017 he was called up to the England squad for the Toulon Tournament – alongside the current United goalkeeper, Aaron Ramsdale – and scored the decisive penalty in the shootout as England won the tournament with victory over Ivory Coast’s U20s.
“It was a privilege to put the shirt on and a privilege to play for England because I’ve been living here for quite a long time now,” Vieira said. “To win the tournament and put the winning penalty away as well, that topped it off.”
Life at Sampdoria began well enough for Vieira, with 15 appearances in his first season and 29 in his second. But he hit the headlines when he was racially abused by Roma fans - "This happens too often, it shouldn't be this way,” he said – and injury restricted him to only five appearances on loan at Verona last season, although one did come against Juventus and his namesake Cristiano Ronaldo in a 1-1 draw.
He returned to Sampdoria, but his career appears to be at a crossroads. The midfielder is only 22, and it’s easy to see why a return to Yorkshire – where a lot of his family are still based, and where he enjoyed so much success – would appeal, if United accepted the invitation to lodge a bid.