Mkhitaryan has made 94 appearances for Dortmund, scoring 24 goals and providing 20 assists.
In February, Mkhitaryan’s agent suggested his client’s future lay away from Signal Iduna Park: “Henrikh wants to leave Dortmund at the end of the season. We will have to wait and see what we can do.
Liverpool have made seven signing in this window so far with James Milner, Danny Ings, Joe Gomez, Adam Bogdan, Nathaniel Clyne, Roberto Firmino and Christian Benteke.
Liverpool already have three attacking midfielders in their squad with Philippe Coutinho, Adam Lallana and new signing Roberto Firmino, and if the news is true it will be a major headache for Rodgers for his team selection if Mkhitaryan arrives at Anfield.