The Iranian striker has been missing for the past three weeks with an injury suffered while on international duty in Turkmenistan.
The initial prognosis estimated a recovery period of up to four weeks.
Over the last few days, Azmoun has ramped up his workload in training, reports Il Tempo, and was partially involved in group training activities on Tuesday.
He is expected to be called up for Roma’s upcoming match with Bologna in Serie A on Monday.