Burnley won three of their first nine league matches this season but losing their next seven meant they plunged into the relegation zone.
Despite five draws in their next seven matches, including defiant performances against Manchester United and Liverpool, a 3-0 thumping by Sunderland followed by a loss to fellow strugglers West Ham led to some fans calling for Parker’s removal.
He expressed his frustration at those chants, and chairman Alan Pace supported Parker in a BBC Football Focus interview, comparing protesting fans to children.
Parker had replaced the departing Kompany before the 2024-25 season.
Despite the sale of key players that summer, including Wilson Odobert, Sander Berge and Vitinho, Parker guided the Clarets to automatic promotion, losing out on the Championship title to Leeds United on goal difference.
His side kept 30 clean sheets in 46 league matches – the most in a season in the history of the Championship.
However, Burnley have conceded 68 goals in 34 league matches this campaign – the most of any side.
Last season was Parker’s third time winning promotion to the top flight as a manager, having done so with Fulham in 2020 and Bournemouth in 2022.
He has also managed Belgian side Club Brugge, but was dismissed in 2023 after winning two of 12 matches in charge.
Parker played for Charlton, Chelsea, Newcastle, West Ham and Tottenham before turning to management.
He also made 18 appearances for England.