Ayew, 26, has been given extra time off after representing his country during the 2017 Africa Cup of Nations qualifiers.
The Ghana international underwent test at the club’s Landore training ground on Monday.
The former Marseille versatile man is believed to be angling for a move away from the club after a fabolous debut campaign.
The deputy Black Stars captain has emerged on the radar of several top clubs and fueled speculation when he stated he was keen on playing Champions League football.
But at the moment, he will return to pre-season with the Swans before holding a showdown talks with the club chairman Huw Jenkins over his long-term future.
The Ghanaian super star joined the South Wales club from French giants Marseille, where he shone on his debut season.