Here, Press Association Sport looks at the contenders to replace Hughton at the Amex Stadium.
That loss, coupled with a terrible run of form that saw Brighton win just two out of their 18 Premier League games, prompted chairman Tony Bloom to bring an end to Hughton's four-and-a-half year reign, having survived relegation by the skin of their teeth.
Potter, 43, signed a three-year deal when he left Sweden for Swansea in June 2018.
Swansea have not commented, but are aware they will have a fight on their hands to keep Potter if he is offered the chance to manage in the Premier League.
Potter insisted he was focused on progressing at Swansea after being linked with Celtic in April.
"Chris will always be very fondly remembered by Albion staff and fans as one of our club's finest and most-respected managers".
"I would like to wish Chris, Paul (Trollope) and Paul (Nevin) - who have all worked extremely hard throughout their time here - every success for the future, and thank them on behalf of everyone at the club".
England Women's manager, Phil Neville, who is preparing to take the Lionesses to the World Cup this summer is next in the market, at 11/2, with the third favourite also from the worldwide arena, Northern Ireland boss Michael O'Neill, available at 14/1.