Graham is available on a free transfer.
The tabloid claims that Rangers have identified the 30-year-old as the ideal partner for this season's top scorer Martyn Waghorn, who like Graham hails from England's North East and has also played for Sunderland.
The Gers may have the edge over their city rivals Celtic, with manager Mark Warburton knowing Graham from his time coaching at Watford.
But the possible appointment of Brendan Rodgers at Parkhead could throw a spanner in the works, as the Ulsterman was Graham's manager at Swansea City - paying £3.5 million to prise him from Vicarage Road.
And the former Middlesbrough front man is familiar with another name in the frame for the Celtic hotseat, having spent the past four months playing under Paul Lambert at Blackburn - where he has scored six goals in 17 appearances.
Rangers sealed their promotion to the Premiership last month and are expected to challenge the Bhoys for the title next season.