Although it is not thought any substantial bids were made for the midfielder, he did attract interest with Arsenal and Manchester United reportedly keeping tabs on him.
Wolves, however, were able to keep hold of the 24-year-old and he has since made a superb start to the season.
When asked how influential he can be for the team moving forward, Lage said: “It depends on him. If he continues to play well he can continue to be part of the project.
“The most important thing is the next day. I see him training very hard with a big ambition to improve himself.
“If you’re training the way he trains, he plays the way he’s playing. But in this life, after the big teams come for this player.
“I live with the rumour that he can leave, but he stayed with us and I think he took the best decision.
“To go, just to go – don’t go, stay. Continue to improve with us and help us to get better. Let’s see what happens. If the club has a good project, as it does have, we also need to conquer this with the players.
“The project should be Wolves going to the next step. What Nuno did was very good and I want to continue with that.
“From the club’s side, we need our players to stay with us. Not just with the contract and salary, but with more ambition to be better.”
Meanwhile, Lage was not drawn on whether he wants to keep Joao Moutinho, who is out of contract at the end of the season.