The club's captain has not featured since sustaining the problem in the 2-0 win over Napoli in October.
Prior to the victory, the 37-year-old had started six Serie A games for Rudi Garcia's men, scoring three times.
In a statement on their website, Roma said that Totti had undergone tests, which revealed promising results, adding that he will be the subject of further examination next week.
"This morning (Monday), as part of his recovery program, Francesco Totti - with the agreement of the AS Roma medical staff - underwent a scan and had a check-up with Professor Mariani," the statement read.
"Results showed the player's fitness has improved and he will increase his workload on the field from tomorrow.
"He will undergo further tests in around seven days."
Despite Totti's absence, Roma remain top of the league and are yet to lose in the top flight this season.
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