The Mirror says the former Swansea frontman has failed to find the net for the Black Cats since his ¬£5million move to the Stadium of Light 18 months ago.
Graham spent time out on loan at Hull and Middlesbrough last season, but returned to Wearside in the summer.
However, the 29-year-old has featured just once for the Sunderland first team so far this campaign, appearing as a late substitute in the Capital One Cup defeat against Stoke last month.
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