Dobbie missed Monday's play-off final win over Watford after his loan stint from Brighton expired, but he played a big part in their successful promotion to the Premier League.
The Scot scored three goals in 15 appearances for Palace and Eagles boss Ian Holloway is a huge fan of the attacker having also worked with him during his time in charge of Blackpool.
Dobbie joined Palace on transfer deadline day in January after finding himself down the pecking order at Brighton and the Seagulls are thought to be willing to let him leave.
The 30-year-old is believed to have agreed a two-year deal at Selhurst Park as Holloway begins his plans for life back in the top flight.
For Dobbie it was his third successful promotion to the Premier League after previously enjoying promotion with Blackpool and Swansea.