Graham, who took charge of 200 bouts – including championship clashes – during a 12-year career, is keen to make his mark as a promoter and wants the Gilmerton fighter on board.
Graham said: "I am serious about my quest to relaunch both my career as a promoter, after turning in my ref's license, and relaunching Jason's career.
"As I've told him, his career has seriously stalled as he has fought once over the last two years."
And the Fauldhouse-based businessman added: "I've drawn up a plan to promote in eastern Scotland which will guarantee Hastie regular ring work as part of these show bills and I've had to put up 12,000 of my own money as a promoter's financial bond to the Board of Boxing control. I've even offered Hastie an option to leave me after 12 months and go with a bigger promoter once he wins his first three bouts under my promotional banner."
Meanwhile, Hastie commented: "Paul Graham's offer definitely interests me and I hope to tie things up with him soon. I'm really fit as I've been training with ex-world champion, Paul Weir, but I can't wait to get back into ring action and earn some much needed money again.
"Paul has told me that he's promoting his first show really soon and I'd definitely like to be on that bill."