The 35-year-old midfielder, who has been impressive so far this season, is out of contract this summer after joining Wolves in 2018.
It is understood an offer is on the table for fellow out of contract player Romain Saiss, while it is believed some talks have begun with Moutinho – however it is not expected any terms will be agreed imminently for either player.
When asked if he hopes to keep Moutinho beyond this season, head coach Lage said: “I hope so.
“The only thing I can say from my point of view as a manager is that I’m really very happy with him, his performances and the way he works every day. He is a professional.
“He is an important player because of the experience he can give us. We have a young squad and when we have a player who has played in different countries, for the national team and is 35 with a long career, he has the experience to give tips to the other guys.
“He is also a good example of what a professional should be. At 35, the way he is playing and training every day, it is the best example we can have here with us.
“He is also a lovely guy and we can talk with him about a lot of things and football in general. He understands football, not just his position but in a tactical way. He’s very important for us.
“I really don’t know where he gets that energy from.
“We need to manage him but every day he is training very hard and wants to win. I don’t know if when he is playing with his kids he wants to win the way he wants to win here.
“If you make it one against one, three against three or five against five, he wants to win every time. That’s the mentality we want and he has that, that’s why he’s a good example.
“He’s a top player. When you work with him every day you can see how important he is and how much he understands the game.
“He is clever. I am very happy to have him here with me.”