"Peter will go down there to discuss terms and he'll take in the FA Cup replay with Manchester City," Kilmarnock general manager David McKinnon told BBC Scotland.
"Given the player's contractual situation, Kilmarnock are delighted with the offer we have had and hopefully the player and his agent will be able to negotiate a satisfactory package for Peter.
"I think it is a great move for him but if Peter decides it is not for him at Leicester then he is more than welcome to come back to Kilmarnock and sign for us."