The 37-year-old has been sidelined since his team's 2-0 triumph over Napoli on October 18.
A statement from Roma read: "As part of his recovery program, Francesco Totti underwent a scan and had a check-up with Professor Mariani.
"Results showed the player's fitness has improved and he will increase his workload on the field from tomorrow [Wednesday].
"He will undergo further tests in around seven days."
Totti is expected to miss three more league games but could recover in time to play at AC Milan on December 16.
Roma, who lead the Serie A standings with a one-point advantage over Juventus, are unbeaten this season and take on Cagliari on Sunday.