"We're in serious negotiations and expect to complete them by next week some time," Rahman's manager Steve Nelson said Friday. "We are pretty close to finalizing the deal."
Nelson said the fight would be scheduled for May and take place in Istanbul, Turkey.
Rahman (41-6-2), the WBC's fourth-ranked contender, hasn't fought since losing his title to Oleg Maskaev in August.
The Turkish-based Sam (27-3-0) is the third-ranked contender and the WBC's international heavyweight champ. Since losing to Maskaev in November 2005, Sam is coming off three straight victories, including a 12-round unanimous decision over Bob Mirovic in November.
It's possible that one or both fighters could move up a notch in the rankings now that top-ranked contender Samuel Peter has defeated No. 2 James Toney for a second straight time earlier this month.
Citing undisclosed problems, Nelson also said Rahman is pulling out of a scheduled fight against Ray Mercer, which was to take place at the Mountaineer Race Track in Chester, W.V., on Feb. 22, and broadcast on cable network Versus.
"It had nothing to do with money. It had to do with the fact that (Rahman) had some problems and we're not going to take the fight unless he's 100 percent," Nelson said.
Rahman's departure leaves the West Virginia event without a headline fight.
Versus spokeswoman Katie Bradshaw said the network is seeking to line up a new main event.
Buffalo heavyweight Joe Mesi (33-0) will be featured on the undercard. His father and manager Jack Mesi announced Friday that Mesi will fight journeyman George Linberger (29-8-1) in a scheduled 10-round bout.
It's the fifth - and longest - fight in Mesi's comeback bid since he had his medical suspension for a brain injury lifted last February. The WBC's former top-ranked contender, Mesi had been out of boxing after sustaining at least two subdural hematomas - bleeding on the brain - in winning a unanimous decision over Vassiliy Jirov in March 2004.
The 33-year-old Mesi is currently training in Puerto Rico. He hasn't fought since Sept. 15, when he won a unanimous decision over Jason Weiss