Drummy, 53, has been at Stamford Bridge since 2007 in a variety of roles, most recently reserve team manager before taking on his current position over the summer.
Palace had been on the brink of appointing Malky Mackay on Wednesday but his name appears now to be firmly out of the frame after Cardiff submitted a dossier to the Football Association alleging misconduct against their former manager.
The dossier also brought an end to Palace sporting director Iain Moody's time at Selhurst Park.
Mackay's downfall left former Spurs boss Tim Sherwood as favourite with the bookmakers to take over from Tony Pulis, who stood down from the role last week after showdown talks with owner Steve Parish.
Drummy's playing background was mainly in non-league football, although he did play five times for Blackpool, but since his retirement he has built a decent CV as a coach, first with Arsenal where he played a part in developing a number of players who went on to represent their first-team.
He moved to Chelsea as assistant to Paul Clement in the Chelsea U16 squad and took over when Clement stepped up.
Drummy took over from Steve Holland as reserve team manager, as well as overseeing the U19s in their NextGen Series matches, and assumed responsibility for the club's growing number of overseas partnerships earlier this summer.