The 29-year-old has impressed both the coach, Jose Mourinho, and the club despite playing very limited minutes in the first months of this season.
His appearances off the bench have often resulted in Roma getting a result near the final minutes of almost any game he has featured in.
According to Corriere dello Sport, Roma would like to include Azmoun in its long-term plans.
However, for the time being the club has not taken a decision yet as to whether trigger the option in his loan from Bayer Leverkusen or not.
Azmoun’s current price tag is €13 million –a fee that Roma will not be able to afford if it fails to qualify for the Champions League.