The 22-year-old is being chased by a host of Premier League clubs following Cardiff's relegation to the Championship, but Crystal Palace are hoping to secure a deal ahead of their rivals.
QPR, Arsenal, Liverpool and former club Spurs are also tracking the England defender who has a release clause of £8 million.
The young defender will improve any side's defence ahead of the new season and The Eagles are believed to have made contact with Cardiff to express their interest in Caulker, as well as striker Fraizer Campbell, who has an £800,000 release clause.
Palace want to secure a double signing from The Bluebirds for the two Englishmen, a bold move considering the tensions between the two clubs last season.
Cardiff will not accept an offer below the release clause set on the player who only joined the club last summer, following an £8 million switch from Tottenham Hotspur in a move that Caulker hoped would give him a chance of regular first-team football ahead of the World Cup.
He didn't make Roy Hodgson's World Cup squad for the tournament this summer, but Caulker played in every Premier League game last season for Cardiff, scoring five times along the way.
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Caulker was a standout performer for The Bluebirds despite their relegation from the Premier League and he will improve any side's backline ahead of a proposed switch this summer.
Will Crystal Palace win the race for Caulker?