Dimitry Seluk, who represented Mkhitaryan at the time, claims that the Armenian international would have moved to Anfield if their relationship had not broken down.
"Eventually, we parted ways with him because of that whole situation," Seluk told TheseFootballTimes.
"Obviously, by that time, Mkhitaryan had already become a well-known player, and when Borussia Dortmund offered Shakhtar €27m (£23m) for Henrikh, suddenly [Mino] Raiola was all over him.
"Although I had already talked to Liverpool who were also interested in Mkhitaryan and wanted to sign him.
"If Henrikh hadn't lied to me and we hadn't parted ways with Henrikh, he would have been a Liverpool player."
Mkhitaryan is now an Arsenal player, having signed for the club as part of the January deal which took Alexis Sanchez to United.