It’s understood the Premier League side have given Kavanagh the opportunity to do some training with the club.
Kavanagh (20) actually spent the majority of this season in the First Division with Shamrock Rovers II and consistently stood out.
He was shortlisted for player of the year at that level in the PFA Ireland awards but the playmaker was also included in the final three for the overall young player award that was open to players in both divisions.
Kavanagh has been around Ireland U-21 squads and is regarded as one of the most technically-assured youngsters on the Irish scene.
There is an Irish link at Palace with former Rovers favourite Stephen Rice now working as a development coach with their U-23 team.
Thomas Oluwa, another promising youngster in Tallaght that has found it hard to get chances with their title-winning team, is also on the radar of English clubs but an end-of-season injury came at a bad time for him.
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Meanwhile, Brighton are interested in young Rovers keeper Killian Cahill.
The Seagulls have tracked the progress of Cahill who has come through the Rovers ranks and was recently on the bench for their FAI Cup semi-final with Sligo Rovers when Leon Pohls was ruled out at the last minute.