The 18-year-old midfielder has been a standout performer in his native Brazil this season and has received interest from a host of top European clubs.
Maia's agent Alexis Malavolta revealed the Red Devils and Blues, along with Premier League rivals Arsenal, are among the teams keeping tabs on his client.
"When there were six months left to the end of our client Thiago Maia's contract (the deal was set to end in December), we had official bids from Atletico Madrid, Juventus, Monaco and Arsenal. He chose to renew it and he's very happy at Santos," Malavolta told Sports Witness.
"Currently there are many clubs from Germany, Italy, England and Spain coming to Brazil to watch Santos games and especially see our client's development.
"Now with the call up to the Olympic team, the interest from more clubs grows because of the visibility. We believe he will get to the national team soon.
"For now, no official interest or official bids have come. But if they come, I'm sure Thiago Maia will analyse it very carefully."