However, with the first instalment of Darren Bent's transfer fee having barely covered the money Sunderland owed to Tottenham, boss Steve Bruce has warned the club's fans not to expect a "£20m marquee signing" this month.
Having contacted a large number of clubs in the wake of Bent's £24m move to Aston Villa, Bruce has gradually whittled down his list of targets to a handful of players.
One of those slipped through the net yesterday, with John Carew agreeing a loan deal with Stoke despite competing interest from Wearside.
Carew's arrival in the Potteries will, however, increase Sunderland's chances of landing Fuller, a 31-year-old Jamaica international who will be available for around £1.5m, and Tuncay Sanli, who cost the Potters £5m when he left Middlesbrough in 2009.
A double deal is possible, although Bruce may opt to plug a short-term gap with Fuller and keep the rest of his powder dry ahead of an anticipated big-money move for a more established forward in the summer.
"I've had a conversation with Tony (Pulis, Stoke boss) to see whether Fuller might be available and it might be a possibility," said Bruce, who will be without Danny Welbeck for up to two months after the striker underwent surgery to repair torn knee cartilage. "He's one of the names in the hat because I believe he's available. He's been a good Premier League player and I like him.
"We're pushing, but it's difficult. There's still ten days to go though. We might have to be without someone this weekend, we'll see.
"But we've cast the net far and wide, and there are two or three irons in the fire. It's like puppies at Christmas though - you don't just go and buy one for the sake of it."
Stoke assistant Dave Kemp last night played down the likelihood of Fuller leaving the Britannia Stadium - "He is our player, and he has every chance of being involved on Saturday" - but confirmation of Carew's transfer should see a shift in the Potters' stance.
Sunderland are also hoping for a softening of Paris St Germain's increasingly entrenched position over Sessegnon, and further progress in their continued pursuit of loan target Muntari.
The French club are adamant Sessegnon, a 26-year-old Benin international, will not be leaving on loan this month, forcing the Black Cats to consider a permanent move for a player who can play on either the left or right of an attacking three.
Having previously threatened to go on strike if Paris St Germain blocked a move to England, Sessegnon returned to training yesterday, but Sunderland officials are hoping to hold further talks before the weekend.
"He's a versatile attacking player, and that's ongoing as we speak," said Bruce. "But it's been ongoing for a couple of weeks now and nothing has really changed. It could be a loan or a permanent deal, but we're still talking."
Bruce, who is increasingly confident of signing Muntari from Inter Milan, has also renewed his interest in Wigan midfielder Charles N'Zogbia, and Latics chairman Dave Whelan yesterday conceded the Frenchman could leave the DW Stadium this month.
"I've always said to Charles if a top-six club comes in for him, he can speak with them," said Whelan. "We'll never stand in a player's way." Nevertheless, Wigan will have to significantly reduce their £9m asking price for Sunderland to do business this month.
At the turn of the year, Bruce had been anticipating a quiet January. That changed on Sunday evening, when Bent submitted a written transfer request hours after the Wear-Tyne derby with Newcastle, and the remainder of the transfer window will be about limiting the damage inflicted by the England international.
Bruce clearly feels personally betrayed by Bent, who was formally unveiled as a Villa player less than two days after he is supposed to have made his first contact with his new club.
Indeed, the transfer was completed so quickly that Sunderland were not even to able to make a counter-offer to the striker and his representatives.
"Everybody connected with Sunderland is disappointed with the way it was done," said Bruce. "It's left a sour taste. There's been a lot said about tapping up and things like that. I don't want to get into that, but it's happened so quickly that it's breathtaking.
"The most disappointing thing is that Darren made his request even though he knew we were in a difficult situation with all the injuries. We fought off a rival bid from Turkey (Fenerbahce) last summer, so we can't really understand the timing of this all coming round again.
"If Darren had come to me and said he was unhappy six weeks ago, it would have given me time to work around things and grant his wish. But the speed and timing of all this has dropped us in it. You'll have to ask Darren why he didn't wait another three months to the summer and show us more respect.
"I also can't go along with the idea of him having moved to a bigger club who can help him achieve his ambitions. We're trying to play in Europe and Villa are in a relegation battle, so that doesn't make sense."
* Sunderland goalkeeper Trevor Carson has joined League Two side Lincoln City on a one-month loan.