The Gateshead-born striker has enjoyed an impressive run of form at the Liberty Stadium, striking interest from a number of Premier League clubs including Newcastle, QPR, Norwich and Reading.
Graham joined Michael Laudrup's Swans side in 2011 after making a £3.5m move from Watford, and has scored four goals in his last five games.
The 27-year-old has had limited opportunities under Laudrup after being forced to play second fiddle to Michu in attack, but is reportedly unable to leave Swansea until a replacement is found.
Stoke's Kenwyne Jones is Graham's purported replacement, with the Potters striker set to be given permission to talk with Swansea despite being a first team regular at the Britannia Stadium.







