Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
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.