The 31-year-old joined Roma on loan from the Gunners last summer and has made 20 appearances during the 2019-20 campaign, contributing six goals and four assists.
The Italian giants are allegedly keen to sign the Armenian on a permanent deal, but according to Corriere dello Sport, the two clubs are some way apart in their valuation.
Indeed, the report claims that the Serie A side only want to spend €15m (£13.7m) plus add-ons on the attacker, but Arsenal are demanding a figure in the region of €24m (£21.9m).
Mkhitaryan, who moved to the Emirates Stadium in January 2018 as part of the deal that took Alexis Sanchez to Manchester United, has scored nine times in 58 appearances for his parent club.
I Giallorossi are also seemingly attempting to sign on-loan defender Chris Smalling from Manchester United.