The former Italy star has spent his entire career to date at the Stadio Olimpico, making almost 700 appearances for the capital club over the course of the last two decades.
His current deal expires at the end of the season but he is close to extending his stay with his boyhood club.
"We are sorting out the final details," the 36-year-old told reporters. "There isn't a lot to do. We'll watch for the president now to make a decision on when to put pen to paper."
Meanwhile, general director Mauro Baldissoni also said that a new deal for the former Italy international was imminent.
"There are just the fine points remaining to sort out," he said. "He will soon sign the contract. There are no problems."