The 31-year-old signed a short-term deal back in the summer, with Millwall making their move in September.
He was handed a contract until January 2018 but he has yet to make an appearance for the Lions this season.
The former MK Dons star is behind Jordan Archer in the pecking order but Harris has been impressed with his attitude and wants to reward him with fresh terms.
Harris told News Shopper: “There have been really positive discussions. I want David to stay. He’s done really well.
“He’s a top quality goalkeeper with a point to prove at this level. I’ve got two young goalkeepers in Jordan Archer and Tom King who have got huge potential.
“We just felt we needed a little bit of experience in that department and that’s not changed whether that’s in the team or training group. Dave certainly gives us that.”
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.