Birmingham officials are understood to have tabled an £11m offer for Jones, but Black Cats boss Steve Bruce has been reluctant to sanction the striker's departure without a replacement in place.
However, the last 24 hours have seen Sunderland close in on Kuranyi, and even though the 27-year-old conducted an interview with Schalke's official website last night in which he spelled out his desire to remain with the German club, Jones' departure now appears all but inevitable.
Stoke City are expected to make an offer of their own having monitored the Trinidad & Tobago international, but Birmingham have leapt to the front of the queue and boss Alex McLeish is confident of tying up a deal within the next seven days.
McLeish has up to £40m to spend following Carson Yeung's takeover, and is willing to commit more than a quarter of that sum to the capture of Jones.
He has also inquired about Newcastle's Andy Carroll, but Jones' Premier League pedigree has taken him to the top of McLeish's wanted list.
The Blues boss has instructed his club officials to make an £11m offer for the 25- year-old, and while he refused to confirm the existence of a bid at his weekly press conference yesterday, he made little attempt to distance himself from the speculation.
We've made inquiries about a lot of people, said McLeish. I don't want to confirm or deny a bid has gone in (for Jones).
Jones came close to leaving the Stadium of Light last January, when Tottenham lodged a £15m offer, but then manager Ricky Sbragia persuaded him to sign a four-and-a-halfyear contract.
His form has dipped since then, though, and Bruce has privately harboured doubts about his suitability from the moment he arrived at the Stadium of Light in the summer.
Jones has scored six goals in 19 matches this season but, tellingly, Bruce has dropped him to the bench on a number of occasions and opted to play Darren Bent as a lone centreforward.
Jones' future is dependent upon Sunderland's attempts to sign a striker, however, and Kuranyi has emerged as Bruce's leading target.
The Schalke striker is out of contract in the summer, and the Black Cats are ready to lodge a £3.5m offer.
A number of Premier League clubs, including Everton, Blackburn and Fulham, have inquired about Kuranyi's availability, but none are willing to pay more than £3m for a player who will be free to move for nothing in the summer.
Sunderland would be willing to go to that price, and the Black Cats are also in a position to match the German's wage demands.
Kuranyi is understood to be aware of the Wearsiders' interest, and claims to be keen to remain with his current employers.
I try not to get involved in it too much, he said last night. I want to have success with Schalke. We are in a very good situation at the moment.
I have already had success here for three-and-a-half years and have also experienced difficult situations, but I feel good here and am committed to Schalke.
However, with Schalke officials keen to secure a transfer fee rather than allow his contract to expire in June, yesterday's committed comments could count for little.
Kuranyi is far from Sunderland's only target, and Bruce is understood to have inquired about three different right-backs as he attempts to bolster his side's defence.
Initially, he attempted to sign Tottenham's Alan Hutton on loan, only to be told that Spurs would only be willing to sell him for £4m.
He then turned his attention to former Newcastle right-back Habib Beye, only for Villa boss Martin O'Neill to scupper his hopes of a quick deal by refusing to sell the Senegal international before he had an opportunity to bring in defensive reinforcements of his own.
Therefore, Bruce has approached German club Hamburg to sound out the possibility of signing Ivory Coast international Guy Demel.
Demel, who is currently representing his country at the African Cup of Nations, spent a year at Arsenal in 2000 without featuring in the senior side, but has subsequently carved out a formidable reputation in the Bundesliga.
He can also play in a defensive midfield role, and Bruce has not been put off by the £5.5m price tag.
Sunderland have extended Jack Colback's loan at Ipswich Town until the end of the season.
A Safety Advisory Group meeting today will determine whether tomorrow's home game with Bolton will go ahead as planned.
While there are no issues with the pitch, problems are anticipated on surrounding roads that could prevent supporters, emergency services and club personnel from getting to the game.
We will continue to monitor the weather conditions and associated safety issues,
said Ken Scott of Sunderland City Council, who chairs the Safety Advisory Group.