There was also interest from Bristol City in the former Wolves and Blackpool defender but the Robins are due to appoint former Barnsley manager Gerhard Struber as Liam Manning’s replacement in the next 24 hours.
Edwards guided Luton to promotion to the top flight for the first time in more than 30 years in 2023 when they beat Coventry on penalties in the Championship play-off final.
Luton finished 18th in the Premier League in 2023-24, six points from safety, and were relegated.
He left in January with the Hatters 20th in the Championship and they ultimately dropped into League One last season, suffering back-to-back relegations.
Former Wales international Edwards also took charge of England Under-16s before being appointed Forest Green manager and leading them to the League Two title in 2022.
He joined Watford that summer but was sacked in September after just 11 games, and joined Luton two months later.
