Pardew took over at Palace in January and rescued the club from relegation.
The experienced coach would be reunited with former striker Demba Ba who he coached during his time in charge of Newcastle United.
Beşiktaş are an ambitious club set to unveil a brand new 41,903 seater stadium on the shores of the Bosphorus and aiming for the league title as well as European glory next season.
The lure of coaching a side pushing for the league title could lure Pardew according to reports however, Beşiktaş have yet to officially even register interest in the Palace head coach.
Beşiktaş are currently third in the Süper Lig and crashed out of the title race after losing 1-0 against Konyaspor on Monday 18 May.
The Black Eagles can still finish in a Champions League spot depending on the results from their final two games.