The 27-year-old has travelled with the Swansea squad ahead of the Barclays Premier League meeting with the Black Cats and is available for selection.
Swansea denied reports he had expressed a desire to leave when contacted by Press Association Sport and chairman Huw Jenkins told BBC Radio Wales: "At the moment there is no substance to this whatsoever."
But Graham, who is is thought to be keen on the chance to return to his native north-east, could yet be on his way to the Stadium of Light following a protracted transfer saga that has run throughout the January window.
However, Swansea are in a strong bargaining position. The club have no need to sell Graham, who was the club's record signing when he arrived from Watford in a £3.5million deal in 2011 and has two and a half years left on his current contract.
Swansea manager Michael Laudrup would also be loathe to let Graham go with such little time in which to find a replacement.
The Swans had received bids from Sunderland and Norwich earlier this month and Laudrup has made it clear an increase will be required if Graham is to leave south Wales.
Laudrup also expressed puzzlement as to why it has taken Martin O'Neill, who has let Fraizer Campbell, Louis Saha and Ji Dong-won all leave, so long to act given the speculation linking Graham with Sunderland has gone on throughout January.
Speaking prior to reports of Graham requesting to leave, he said: "Even if a player were to say 'I want to leave', it is still between the clubs.
"I will understand it because I don't want players who are unhappy who have a very good chance of going somewhere else."