The duo previously worked together during Rodgers's time at Swansea City, with the 30-year-old striker scoring 12 times in the Swans' first season in the Premier League to help keep them in the top flight.
Graham has found first-team chances limited at Sunderland and spent the second half of the season 2015-16 season on loan at Blackburn Rovers, netting seven goals in 18 Championship appearances under Paul Lambert.
Rodgers, who was officially unveiled as Celtic boss this week, has hired Chris Davies as his assistant, having also worked with him in South Wales, and the 43-year-old seemingly wants Graham back on board too.
Suffice to say that the speculation did not go down well with a lot of Celtic fans on Twitter, many of whom do not seem to be sold on the idea that the former Watford marksman is right for Paradise.
Please Brendan DO NOT sign Danny Graham— The Celtic Family (@CelticFamily_) May 26, 2016
celtic better no sign danny graham.ffs.he was past it 6yr ago ffs— Mick trainer (@michaelt1967) May 26, 2016
No sure how I feel about the Danny Graham link— Scott McFadyen (@ScottMcFadyen97) May 26, 2016
"Brendan Rodgers wants to make Sunderland striker Danny Graham one of his first signings for Celtic" pic.twitter.com/hNUh9dVkbV— Dom Schiavone (@Shiv1888) May 26, 2016
I'm going to just assume that the Danny Graham thing is the media clutching at straws, due to BR working with him in the past.— William (@ThatGuyGoldie) May 26, 2016
Yesterday Tom Carroll today Danny Graham! Gonna be a long summer!— Stephen Smith (@steviereigate) May 26, 2016
Danny graham? Sat on the fence with that one could be good but could just see him being just another Kazim Richards— Izaguirre fan Bhoy (@CameonSimpson) May 26, 2016
A genuinely hope we don't get Danny Graham! He's no the type of player whos gonna get ye into Europe..— Johnston Cochrane (@JohnstonCochran) May 26, 2016
Sorry to rain on the parade.......but Danny Graham?— Eeramacaroonbar (@Eeramacaroonbar) May 26, 2016