The Republic of Ireland international is on a season-long loan at the Britannia Stadium from Aston Villa, where his contract is up at the end of the campaign.
Potters manager Mark Hughes said: "We're trying to do something with Stephen if we can. I know we've had discussions with his people and I've spoken to Stephen myself.
"I think there's a willingness on both sides to get something done. Nothing's been agreed formally yet but I think the intention is there to try to do something if we can."
Hughes is keen to do business in the window, with a striker the top priority, but he dismissed rumours midfielder Wilson Palacios could join Real Betis on loan.
The Welshman said: "That's news to me. There's been no contact as far as I'm aware. Jamie Ness has gone out on loan but at the moment we don't anticipate anybody else (leaving)."
Hughes, meanwhile, revealed Stoke are likely to make a complaint to the Football Association regarding Tottenham's response to Charlie Adam's tackle on Paulinho.
The Spurs midfielder is expected to be out for around a month following Adam's challenge in Stoke's 3-0 defeat last weekend, which was missed by the referee.
Tottenham complained to the FA but it did not deem the tackle worthy of retrospective punishment.
Adam is a hate figure for some Spurs fans as a result of previous tackles against Gareth Bale and Scott Parker, and midfielder Sandro posted a picture of himself on Instagram with a message for Adam: "The Beast (his nickname) is watching you."
Stoke were not impressed, and Hughes said: "There's no need for it.
"We were unhappy that Charlie's playing history in recent games against Spurs was brought up, I think by Spurs themselves. That was a little bit surprising.
"In terms of what the lad (Sandro) said it's unhelpful, and he has to be careful or the FA might look at that situation.
"Our view is that sometimes you can't allow things without responding. I'm not absolutely certain as yet but I think we as a club will respond to what's happened in recent days."
Stoke take on Championship leaders Leicester in the FA Cup third round on Saturday and Hughes' own proud record in the competition means he will be taking the game very seriously.
When asked by BBC West Midlands whether this weekend's fixtures were something Premier League clubs would rather avoid, Aston Villa boss Paul Lambert said: "If they were being honest, they probably would do."
Hughes insisted that was certainly not the case for him, saying: "I've always said there's only certain competitions that we have a realistic chance of having a good run at and the FA Cup is one of them.
"I'm not sure of Paul's record in the FA Cup; from my point of view I was fortunate enough to play in five cup finals and win four of them and it was a fantastic experience, so why would you want to deny yourself and your club the opportunity to go to a cup final?
"It's a marvellous occasion and something, as a football person, you should want to do. I think if you manage your squad well enough then you can have a cup run and you can actually help your league form as well."
Hughes will be without a number of players, with Ireland (hamstring) and goalkeeper Thomas Sorensen (Achilles) joining the injured list.
Sorensen's injury coupled with number one Asmir Begovic's broken finger means Jack Butland will make his first start for the club and 19-year-old Austrian Dan Bachmann will be on the bench.
Hughes will wait for a verdict on Sorensen's likely lay-off before considering bringing in another keeper.
There was good news on key defender Robert Huth, who has returned to training after knee surgery, although he is unlikely to be back in the squad for another two weeks.
Hughes said of his likely side on Saturday: "We'll see how they rock up but if the ones I'm planning to play are okay then we'll go strong."
- Sports & Recreation
- Aston Villa
- Mark Hughes
- Charlie Adam