The 35-year-old has only made five appearances this season and none in the Premier League as fellow shot-stopper Jose Sa has enjoyed a successful first season at the club.
Ruddy signed a one-year contract extension at the beginning of the season and will be out of contract in the summer.
And when asked if he would like him to stay with the club, head coach Lage said: “In my opinion, yes.
“I don’t know what he has in his mind but we need a day to talk about it.
“In my opinion, I am pleased to have John around us.
“He’s one more guy that deserves to play much more. John gives a lot of things and is an important voice in the dressing room.
“He is a leader by example and works hard every day.
“If Jose is having a fantastic season it is because John is there. John is so important for us and I have no problem saying he deserves to play more, but Jose for now is having a fantastic season.”
There is currently an offer on the table for Romain Saiss to sign a new deal, while talks are ongoing with Joao Moutinho – two players who are also out of contract in the summer.
Fernando Marcal is the final senior player who will see his deal expire in the coming months with reports linking him to a move back to Brazil.