Felix, promoted to Benfica's first team at the start of the season, has scored seven goals and set up three more in 13 league appearances.
Diario AS has reported that United are prepared to offer £100 million for the 19-year-old, while Real Madrid and Barcelona are also monitoring him.
"Joao is a youngster with a lot of potential," Lage told a news conference.
"There is a lot of talk about him with respect to many things, but I only like to refer to what he does on the pitch and not what he can do away from it.
"If you know him, he's a youngster that has his feet firmly on the ground. He deals with everything that is going on with total calm."
Lage said he would not be surprised if Felix earned a first senior Portugal call-up for next month's Euro 2020 qualifiers.
Portugal host Ukraine on March 22 before facing Serbia three days later and Lage said Felix, who has scored four goals in nine appearances for the under-21s, was ready for the step up.
"Would it be normal? Yes, considering the work he has been doing," Lage said. "It's what has been happening in the national team, in view of performances, [coach] Fernando Santos has given other youngsters opportunities."
In November, Felix signed a Benfica contract until June 2023 which contains a €120m release clause.
Former Benfica and Sporting coach Jorge Jesus has compared him to both Rui Costa and ex-Brazil international Kaka.
"I'm surprised by a young man, Joao Felix, who is going to be a reference in Portuguese football," he said.
"He still has a lot to learn with respect to movements and tactics, but he will get there. He reminds me of Rui Costa and Kaka -- he has a mixture of the two and is going to be a player above the average."