The person spoke to The Associated Press on condition of anonymity because the contract talks had not been made public.
Iverson, his agent and business manager met with team president Ed Stefanski, coach Eddie Jordan and two other members of the organization Monday during the first formal meeting between the Sixers and their former MVP.
Iverson announced his retirement last week after an ill-fated stint with the Memphis Grizzlies. The 10-time All-Star was NBA MVP in 2001 when he led the Sixers to the NBA finals.
Another person with knowledge of the deal, who also spoke to The Associated Press on condition of anonymity because the talks had not been made public, said Iverson's decision should come Wednesday.
The person says the 76ers are taking a chance on Iverson because he's the best free-agent guard available and the financial commitment is minimal. The Sixers would owe just under $650,000 if they guarantee his contract for the remainder of the season on Jan. 10.
"What is the downside if you can cut him any time you want?" the person said.
Iverson would still need to undergo a physical before the deal is complete. As of Tuesday night, the Sixers had not heard back from Iverson's agent Leon Rose.
Iverson announced his intention to retire last week after no other team expressed an interest is signing the four-time scoring champion. The 6-foot Iverson played three games this season with Memphis before taking a leave of absence to attend to personal matters. He was waived after the two sides agreed to part ways.
He's on the brink of getting a second chance with the Sixers(5-13), who have lost seven straight entering Wednesday night's game at Oklahoma City and need Iverson to spark sagging ticket sales and their playoff chances.
This reconciliation was once thought foolish after their acrimonious split three years ago. Iverson's last game with Philadelphia was Dec. 6, 2006 in Chicago. He refused to play the fourth quarter and was banished from the team two days later. He was eventually traded to Denver as part of the Andre Miller deal, and bounced to Detroit before landing in Memphis.
The Sixers finish their four-game road trip Saturday against the Charlotte Bobcats and Iverson's former nemesis, coach Larry Brown. Brown said Tuesday he was upset that Iverson's best option was a non-guaranteed deal.
"I get worried about that message, but I also admire Philly for giving him a chance," he said. "That's more meaningful for me. I look at a guy that scored 20,000 points and played hurt and did so much and now he's got to play for a non-guaranteed contract, that's pretty troubling for me."
If Iverson accepts the offer, his likely debut would come Monday night at home against Denver. In a double-dose of intriguing timing, the Sixers play at home Dec. 9 against Detroit.
Perhaps Iverson will show his former teams that he still has something left in the No. 3 jersey.
Or, the Nuggets and Pistons will see they made the right choice to move on without the controversial guard.
CSNPhilly.com first reported the offer.
Memphis Grizzlies owner Michael Heisley told the AP on Tuesday that he spent almost an hour on the phone with Stefanski before his meeting with Iverson.
"I told him I thought Allen had the game and I thought he would be a positive contribution to his team and was sorry it didn't work out with us. I thought to get back with Philadelphia, it was a good chance it would work out for them. I feel extremely happy about it," Heisley said.
"Quite frankly, I'm sorry that we couldn't work it out between us and Allen. I don't feel duped. I don't feel upset. I quite frankly arranged for the severance, which we could've stopped, which would've stopped him from being able to play for anybody. I did it so he would have an opportunity to go play."
The 34-year-old Iverson began an indefinite leave of absence on Nov. 7 to deal with a personal issue.
Heisley said he knew exactly what the personal matter was, but he refused to discuss that issue.
"I hope it's cleared up," he said.
Heisley believed Iverson would return at first, then said he thinks Iverson did not want to rejoin the Grizzlies for reasons that could have included retirement or possible interest from other teams.
"I hope he comes back and I hope he has a great career with them," Heisley said.
---- AP Sports Writers Teresa Walker in Nashville, Tenn. and Mike Cranston in Charlotte, N.C. contributed to this report.