The 37-year-old has been out since October 18 after hobbling off in a 2-0 win against Napoli, after scoring three goals and assisting another six in a stunning opening eight games of the campaign.
Scans at the start of November showed signs of improvement for the attacker, and his condition has now improved sufficiently to begin a regime to boost his fitness.
A club statement read: "This morning (Monday), as per his recovery program, Francesco Totti – in the presence of the AS Roma medical staff – had a check-up with Professor Mariani.
"Test results showed the player's condition has improved and, as of tomorrow (Tuesday), he will begin a technical and fitness program aimed at gradually bringing him back into the squad.
It is welcome news for Rudi Garcia's men, who - despite being unbeaten this term - have seen their efforts stall with four consecutive draws in Serie A, leaving them three points behind Juventus.
The capital club will face a challenge to get back to winning ways on Sunday, when they host Fiorentina.
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