The former West Brom boss had emerged as the favourite to succeed Tony Pulis, who made the shock decision to depart the club earlier this month.
Reports suggested the Scot held talks with Palace co-chairman Steve Parish, but speculation is mounting that the Eagles will instead opt for former manager Neil Warnock.
The 65-year-old has been without a managerial job since leaving Leeds United in April last year, but could be on the brink of a surprise return to Selhurst Park.
Warnock took charge of the Eagles from 2007-10, leading the team into the Championship play-offs, but then left after the club fell into administration.
He would rejoin in another period of turmoil, with the club lying in the Premier League drop-zone after the sudden end of the Pulis era.