Wigan Athletic manager Uwe Rosler has admitted that he wants to reinforce his attacking department.
There will be no swap deal involving Fernando Torres and Roma's Mattia Destro, according to the Italian player's agent.
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.