Graham had been expected to return to his native north-east to join Sunderland, who had bid around £5million for the 27-year-old as they look to ease the workload on leading scorer Steven Fletcher.
Graham remains Sunderland’s No1 target during the final week of the transfer window, as Martin O’Neill looks to augment a strike force that has been depleted by the departures of Fraizer Campbell and Louis Saha.
But Graham is growing increasingly frustrated over the hold-up to his potential move to the Stadium of Light, which depends upon Swansea bringing in another striker to take his place.
But it is now thought that a Turkish club have entered the race for Jones, and the 28-year-old is receptive to the idea of leaving the Premier League.
That could impact on Sunderland’s bid to land Graham, with Swansea refusing to sanction the former Middlesbrough man’s exit before they can land a suitable replacement.
The bookies have slashed Norwich's odds from 16/1 to 10/1 on signing Graham before the window slams shut.
But reports also are circulating, that Stoke are interested in the player to.
Stoke City are set to shake up the chase to sign the striker by offering an exchange deal with Kenwyne Jones.
With Swansea’s £3million bid for Jones already having been turned down by Stoke, the Britannia Stadium club are to propose a straight swap deal for the two strikers.