The Armenian joined the Gunners from Manchester United in 2018 as part of a swap deal which saw Alexis Sanchez head to Old Trafford.
However, the 31-year-old has struggled to make a significant impact at the Emirates since his arrival, and was shipped out to Roma on a season-long loan last summer.
According to Gazetta dello Sport, the Italian outfit are keen on signing the midfielder on a permanent basis, and Arsenal's interest in fellow loanee Chris Smalling could play a part in any potential negotiations.
However, the report also claims Paulo Fonseca's side are wary about the player's age, and could potentially think twice about the transfer if Mkhitaryan was to seek a three-year deal.
Despite struggling with injuries this season, Mkhitaryan has registered six goals and three assists in 13 Serie A appearances during the 2019-20 campaign.