According to the Guardian, the Ghana international is close to sealing a move to the Eagles, with an imminent medical on the cards.
The 26-year-old is said to be making a switch to Selhurst Park in a transfer that will see Dutch youngster Jairo Riedewald move in opposite direction.
The news comes after days of intense speculations about Ayew's future follow Swansea's relegation from the Premier League last term.
Last season, Ayew finished top scorer for Swansea in the elite division, hitting seven goals in 36 outings involving 33 starts.
He joined the Jack Army in January last year from Aston Villa.
During his time in France, he played for Olympique Marseille, Lorient and Sochaux.
His older brother Andre, sealed a one-year loan move to Turkish giants Fenerbahce last week.