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This season saw United take the Germany technology company on as sponsors after seven years with car manufacturer Chevrolet.
It's a deal that could net the 'Red Devils' £230 million across five years, but TeamViewer want their brand to be attached to a 'winning project' on the pitch.
Spanish publication El Nacional claim Vinicius is already top of their wishlist after a sensational breakout campaign.
Vinicius arrived at Madrid from Flamengo in a £40 million deal when he was just a teenager and initially struggled.
Inconsistency hampered his start to life in a 'Los Blancos' shirt but it's started to click under Carlo Ancelotti.
Vinicius has scored ten goals and registered ten assists in 18 appearances as Madrid sit top of La Liga and their Champions League group.
Getting him to Old Trafford would prove difficult as his current contract runs until 2025 and president Florentino Perez is a big fan.
It's also unknown if United will shelve the signing following the sacking of Ole Gunnar Solskjaer and imminent arrival of interim manager Ralf Rangnick.
Vinicius recently praised Ancelotti for helping him improve his game.
The 21-year-old told Cadena SER: "They've all helped me - [Santiago] Solari, [Zinedine] Zidane and now Carlo. With him, I have more confidence, more minutes, more time to do things right. After three years training a lot, it has really helped, but now Ancelotti has arrived and has given me the confidence I need.
"Confidence is important for all players, but now I think I'm ready for this role.
"Before, I don't know if I was, but now I am. I am prepared to be at the top and continue to help the team for a long time and many seasons.
"Now I am 21 years old, before I was younger. I came from Brazil at the age of 18. I had barely played a year of first-team football and I came to Real Madrid, the best team in the world with many great players.
"I came to learn. I have learned and I will continue to learn every day."
Madrid are said to be preparing a new contract for Vinicius which would give him the biggest release clause in world football.
Featured Image Credit: PA Images
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