The Eagles will spend Christmas outside the bottom three having successfully overcome a torrid start to the season.
However, Roy Hodgson has made no secret of his desire to recruit a new goalkeeper and may also be interested in reinforcements upfield as he bids to edge Palace further away from danger in the New Year.
According to the Daily Mail, Holy is on Palace's radar following his performances in between the Gills sticks, but the Eagles may face competition for the Czech's signature from Derby County.
The report goes on to claim that Norway international Elyounoussi is also a target for Hodgson, though Newcastle United may also be keeping an eye out on the 23-year-old attacker.
Up next for Palace is a Premier League home game against Arsenal on December 28.