Sherwood has been out of work since leaving his first managerial job at Tottenham at the end of last season, and is now 1/8 to take over at Selhurst Park.
Former Cardiff boss Malky Mackay had been the favourite up until Sunday evening but is now 8/1, as a surge of bets on Sherwood saw him cut from 5/2 to clear odds-on favourite.
Sky Bet’s Dale Tempest said: “There’d already been a fair few bets on Sherwood over the weekend but things really exploded into life late on Sunday night.
“We continually cut the odds through the night but the punters were relentless, backing it all the way in to 1/8 before we managed to stem the flow on Monday morning.”
Palace have been without a manager since Tony Pulis left his post last week, and other contenders to be his successor include Roberto Di Matteo (16/1) and Neil Lennon (20/1).