The 33-year-old's contract with Roma expires at the end of the season, and there seems to be a lack of progression in terms of talks over a renewal.
As a result, Mkhitaryan can sign a pre-contract agreement with a new club during these months up until the summer transfer window.
According to a report from RB Sport (via SiamolaRoma.it), Dinamo Moscow have set their sights on the Armenian and are prepared to offer him a contract, with them leading the race to sign him.
The details of the contract that they are set to offer him are still unclear, and another Russian club is reportedly also interested in signing Mkhitaryan.
The attacking midfielder joined Roma on loan in 2019, but he then joined on a free transfer from Arsenal just a year later.
It is quite surprising that Roma are willing to let him leave on a free transfer, especially since he is a key player in Jose Mourinho, making 31 appearances in all competitions so far this season, getting three goals and seven assists.
A report from La Gazzetta dello Sport (print edition) did claim that Roma value his veteran status at the club and have opened the possibility over extending his stay in the capital for another year, but the club's management reportedly don't want to rush into things and are waiting to see how the season ends before making a decision.
With him currently being available on a free transfer, it will be interesting to see whether he will look for a move to the top five European leagues, or if he will be going to Russia to ensure regular game time.