Ayew, 26, was 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.
But he will now travel to the United States to join his teammate as they prepare for the new season.
The Swans will play two friendly games during the tour against United Soccer League sides Charlotte Independence on July 13 and Richmond Kickers July 16.
Ayew remains a key figure in Francesco Guidolin’s squad having bagged 12 goals for the Club in the English Premier League last season.
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.
Swans’ 23-man squad for US tour:
Josh Vickers, Kristoffer Nordfeldt, Gerhard Tremmel; Stephen Kingsley, Connor Roberts, Angel Rangel, Kyle Naughton, Jordi Amat, Mike van der Hoorn, Federico Fernandez, Joe Rodon; Leon Britton, Jack Cork, Leroy Fer, Nathan Dyer, Jay Fulton, Adam King, Daniel James, Wayne Routledge, Kenji Gorre, Modou Barrow, Andre Ayew, Oliver McBurnie,