The 46-year-old was brought to Palace by now-Everton boss Sam Allardyce, who had also worked with Margetson for three years at West Ham United previously.
The Welshman remains England's goalkeeping coach following Allardyce's stint and it would appear as if the newly-appointed Toffees manager wants him included in his backroom staff.
“I like the people at Everton and wish him every success. I wish they weren’t trying to nick our goalkeeping coach but other than that, I like them," Parish told The Independent.
Alan Kelly was Everton's goalkeeping coach under caretaker boss David Unsworth but nobody on Everton's official website is assigned that role at the moment.
It was Patrick Lodewijks's position, but the Dutchman left Goodison Park when Ronald Koeman was sacked back in October.
The Merseysiders spent £30 million on signing 23-year-old keeper Jordan Pickford from Sunderland in the summer.