Rangers coach Peter Lovenkrands has emerged as a shock contender to take over as gaffer at Kilmarnock.
The Dane currently coaches at Ibrox, where he is highly rated, and he could throw his hat in the ring to replace Angelo Alessio.
The Rugby Park side will give Alex Dyer the reigns for their next three games before the winter break, which includes a trip to Ibrox, but head of football operations will start work on drawing up a shortlist for the job now.
Fowler says the club want someone with knowledge of British, and preferably Scottish, football - with 39-year-old Lovenkrands fitting that mould.
Italian boss Alessio thanked Kilmarnock fans after being sacked on Tuesday for winning just one game in eight despite being fifth in the Scottish Premiership.