It is believed that the extension could be as long as four years, which would tie him to Tigerland until the end of 2024.
The 22-year old has been weighing up his future amid reports that the Blues have made an enticing offer.
Graham has played 12 games for the Tigers this season, averaging 15 disposals and 4.2 tackles per contest.
Graham burst onto the scene in 2017, booting two goals in the grand final win in just his fifth game.
Jack Graham has decided to stay at Richmond. New contract could run up to four years. Great result for the Tigers, with Graham seriously considering a move to Carlton. More to come on https://t.co/z8yG56ep3u
— Sam Edmund (@Sammy__Edmund) September 25, 2020