Eagles boss Warnock, who takes his side to Turf Moor on Wednesday, contacted Coyle to congratulate him on his side's valiant efforts against Tottenham in the Carling Cup.
The Clarets dumped Fulham, Chelsea and Arsenal out of the competition and came within two minutes of overcoming Spurs in an epic semi-final encounter.
Coyle said: "Neil is a fantastic manager and he has shown that consistently over a tremendous career in management.
"I have a lot of time for him and I have to say he went out of his way to ring me about a month ago and compliment the football club and the team after the Tottenham game.
"I picked the phone up and he just said he had enjoyed what we offered in representing the Championship. I thought that spoke volumes for him as a man and I am certainly in his fan club."