Kilmarnock have been linked with Gus MacPherson and Csaba Laszlo after confirming that they are localising their search for a new manager in the wake of the German Thomas Hassler's snub.
Former Kilmarnock player MacPherson, who was sacked as St Mirren manager in May, and ex-Hearts boss Laszlo have since been installed among the favourites for the position.
Rugby Park chairman Michael Johnston said: "Thomas Hassler has informed us he no longer wishes to be considered for the position.
"We have widened the net by looking beyond these shores, now we will look closer to home."
Johnston added: "There's still plenty of time for us to consider our options before making an appointment ahead of the new season."