There were conflicting reports in the local media on Wednesday following the absence of the 26-year-old's name from The Eagles’ list of players registered for the Premier League, FA Cup and League Cup.
However, the source says there is no problem and insists the player could debut for his new side on Monday against Liverpool.
"Jordan Ayew is eligible to play for Crystal Palace throughout this season, so all the reports circulating around are not factually correct," a source close to the player told Goal.
"He was duly registered on transfer deadline day and unveiled to the club's supporters so how come he wasn't registered?
"Everyone in Ghana knows the story behind his transfer so things got delayed a little bit, but everything was successful in the end and he has been with the first team during training sessions ever since.
"Although, he missed the opening day victory over Fulham at the Craven Cottage, it's even likely he may make his debut against Liverpool or in the subsequent games, so there is no cause for alarm," the source added.
Ayew was Swansea's topscorer last season with 11 goals and was also voted as the Players' Player of the Year.