Dunk's Brighton had the Championship's fourth-best defence last season
Palace and Brighton are fierce rivals
However, Paul Barber, the Seagulls' chief executive, says the club have no intention of selling.
"We have received a bid for Lewis Dunk and it has been very firmly rejected without any discussion," Barber told the Argus.
"We are very busy assembling – and soon we will be preparing – our squad for another attempt at securing promotion to the Premier League, our key ambition, so we have no intention of selling Lewis who has been, and remains, a key part of our squad."
Boss Hughton is preparing an assault on promotion next term
Brighton previously rejected a £5 million offer for Dunk from Fulham, however, that was a year ago, and the 24-year-old's stock will have risen considerably since then.
Following the Cottagers' interest, Chris Hughton's side handed Dunk a new five-year contract, which keeps him at the Amex Stadium until 2020.
The Brighton born defender, who graduated the club's academy, made 41 appearances in total last season, and scored four goals.
Dunk puts Brighton ahead in the second leg of their play-off semi-final defeat to Sheffield Wednesday