The Albion want to add attacking firepower to the squad before the Friday domestic transfer deadline.
According to The Sun, the two clubs can agree on a fee for Ayew.
The issue is his £90,000-a-week wage packet at Swansea. It is beyond what Brighton are willing to pay the player.
Unless the 30-year-old takes a pay cut, he will not be able to get back into the Premier League.
Ayew managed 18 goals in the Championship last term.