The 31-year-old is surplus to requirements at Emirates Stadium and wants a switch to Italy, having joined the Serie A side on loan in September.
The two clubs are yet to agree a fee with sources telling ESPN that the Gunners are holding out for around £10 million.
Mkhitaryan has just over a year remaining on his contract and sources close to negotiations have told ESPN that Roma are unwilling to match his salary and have indicated they want financial assistance from Arsenal to complete a deal.
That could come in the form of a lower transfer fee but also by agreeing to top up his wage for the remainder of his contract. No other clubs have expressed an interest in Mkhitaryan and Arsenal are keen to remove him from the wage bill as Mikel Arteta looks to reshape his squad.
Mkhitaryan hinted at the state of negotiations between the two clubs earlier on Wednesday, with Italian newspaper Corriere dello Sport quoting the Armenia international in a message to Arsenal: "My time in London is over, I hope you manage to find an agreement with Roma because my desire is to remain."
Mkhitaryan enjoyed a renaissance at Roma prior to the suspension of football due to the coronavirus pandemic, scoring six times in 13 games.
Mkhitaryan became a peripheral figure under Unai Emery. And in March, Arteta hinted he could still have a future in north London, admitting: "I always like him, he is the kind of player who can fit in any team when he is at his best."
But Arteta plans to make several changes to his squad this summer and needs to raise funds to finance new signings, meaning Mkhitaryan will move on if an agreement can be found.