Graham joined Swansea from Watford in the summer of 2011 for a transfer fee reported by BBC Sport to be worth £3.5 million.
The former Middlesbrough striker had a good spell at Swansea working with Rodgers before leaving for Sunderland in January 2013.
Now at Blackburn Rovers, the 33-year-old striker has spoken fondly of his time working with current Celtic striker Rodgers at Swansea.
Graham told The Telegraph: “It was unbelievable. Especially working with Brendan. From his training and man-management skills, you could see he was going to manage a big club.
"I had several conversations with Brendan and he was so positive in what he said, and how he spoke to you."
Celtic move in January?
Graham signed a new contract with Blackburn in the summer of 2018, but Celtic should make a move for the former Sunderland striker in the January transfer window.
The departure of Moussa Dembele to Lyon in the summer transfer window means that there is a space in the Celtic squad for another striker.
Odsonne Edouard and Leigh Griffiths are the two senior strikers in the current Celtic squad, and the Hoops could do with an experienced player such as Graham.