Liverpool have completed the signing of Croatian centre-back Dejan Lovren from Southampton
Petr Cech insists he is staying at Chelsea and is ready to fight for the No.1 spot in Jose Mourinho's starting XI.
Former Croatia, Everton and West Ham manager Bilic, 44, took charge of Lokomotiv last summer but could only guide the club to a ninth-placed finish in the 16-team Premier League - the club's worst finish since 1991.
A statement on Lokomotiv's official website said Bilic's contract had been cancelled by mutual consent.
His replacement Kuchuk, 53, is the former manager of Kuban Krasnodar, Salyut Belgorod and Sheriff Tiraspol.