Graham has attracted interest from Championship clubs Middlesbrough and Wolves but there is little to no prospect of either moving for the striker if they have to meet his £35,000-a-week wage.
The Journal says Sunderland face a stark choice - allow him to leave while paying most of his wages or retain him as part of a squad where he is unlikely to feature much.
For the big stories and the banter follow us on Twitter: @tribalfootball
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!