The National League North club lost 6-1 to Needham Market on Saturday, but the former Premier League player wasn’t in the dug-out.
He told Telegraph and Argus that he has decided to leave after less than three weeks.
Redfearn took over on January 17 and hoped to turn the club’s fortunes around.
But things have gone from bad to worse for troubled Farsley, who are playing their home matches at Buxton, almost 70 miles away, due to pitch difficulties.
He told the outlet that he had quit on Thursday - but the new has yet to be confirmed by the club.
Redfearn told the Argus that he “wishes all the Farsley supporters good luck going forward” and “thanks the players for their best efforts”.
Celtic sit two points from safety and are next in action on Saturday when they travel to Leamington.