The 27-year-old joined the club in the summer of 2011 when Brendan Rodgers paid Watford more than £3million for his signature.
But since Michael Laudrup took charge, Graham has struggled to command a regular place - starting less than half of their league games so far this term.
Graham's situation has not gone unnoticed, and Sky Sports understands both Reading and Norwich have approached Swansea.
Graham has scored five goals so far this term, including two in his last two games.







