Steve Coppell is on Crystal Palace's list of potential candidates to replace Dougie Freedman, who quit this week to join Bolton.
Coppell would be one of the top candidates if Palace opted for experience, but there is a group of young managers also on their shortlist. Gareth Southgate, Sean Dyche, Paolo Di Canio and Attilio Lombardo have all been linked.
If the club do opt for the vastly experienced Coppell, Palace's most successful manager, it would be a truly remarkable fifth stint as manager at Selhurst Park, which would be some kind of all-time record.
The 57-year-old might be considered in a more senior role as technical director of football, if the club decide to go down that route.
However Coppell was non-committal about the job when contacted by ESPN but refused to rule out a return. "I have great affection for Palace but I am thoroughly enjoying myself at Crawley," he said.
Parish added: "The last four days I haven't spoken to anyone. Steve [Coppell] is certainly someone I will speak to - somebody we will be consulting, and is a possibility."