Leicester have signed Argentina international midfielder Esteban Cambiasso on a one-year contract.
Reports have emerged that the 27-year-old striker expressed his desire to move elsewhere citing "personal reasons", with Sunderland, who Swansea play on Tuesday, the favourites to sign him.
Swansea denied the stories when contacted by Press Association Sport and Jenkins told BBC Radio Wales: "At the moment there is no substance to this whatsoever."
Swansea had received bids from Sunderland and Norwich earlier in January with Graham finding his opportunities limited by the scoring form of Michu.
But the former Middlesbrough, Carlisle and Watford forward has still managed to score seven goals this season, including four in his last seven appearances.
Speaking earlier on Monday, manager Michael Laudrup had made it clear he was happy for Graham to remain at Swansea and did not expect a deal to be completed before the end of the transfer window on Thursday.
"I think maybe nothing will happen," he said. "There have been a lot of questions about Danny but I can only say Danny is here and we want him to stay and we don't want to change.
"He is here and if he comes to me and he wants to leave - and we have a very, very good offer - then we have to look into it, otherwise it could easily happen we will have the same squad on February 1 as we do now."
He added: "I haven't read anything official or in any newspaper or on television where Danny has said he wants to leave, that means he must want to stay and probably he will."