The 25-year-old left long-term club Marseille when his contract expired earlier this month and is understood to be keen on a move to the Premier League over all other possible destinations.
Swansea are in need of bolstering their attacking options this summer, having lost Wilfried Bony to Manchester City in January and his short term replacement, the loanee Nelson Oliveira, having returned to Benfica.
Ayew is believed to be a friend of Swans striker Bafetimbi Gomis and the pair share the same agent, Mark Mackay, who will join Ayew for discussions at the Liberty Stadium.
Ayew’s contract was allowed to run down at Marseille because of reported financial constraints at the club and he was linked with Tottenham and Roma.
The Ghanaian is the son of three-time African Football of the Year winner Abedi Ayew Pelle,??who spent five years at Marseille over two separate spells.
Andre began his senior career at Marseille, with stints on loan at FC Lorient and Arles-Avignon, before scoring over 44 league goals for the French Ligue 1 club.