The Belgians, unbeaten in the domestic top flight but out of the Europa League, said in a brief statement on Thursday that the Spaniard as well as physical conditioning coach Jorge Simo would be leaving the club.
Bruges general manager Vincent Mannaert told Belgium's Radio 1 that the club was in contact with Preud'homme, who was released as coach of Saudi Arabian club Al-Shabab on Wednesday after their elimination in the Asian Champions League.
Preud'homme, capped 58 times with Belgium, steered Standard Liege to their first league title in 25 years in 2008. He has also coached AA Ghent and Dutch side Twente Enschede, winning the domestic cup with both.
"He is a leading candidate," Mannaert said.
Mannaert added that the club's performances had been below par under Garrido with no sign of improvement despite the side sitting second in the Belgium championship, five points behind Standard Liege after five victories and two draws.
They did though exit in the third qualifying round of the Europa League last month at the hands of Slask Wroclaw.
Bruges reached the finals of the UEFA Cup in 1976 and the European Cup in 1978, each time losing to Liverpool, and have been Belgian champions 13 times.
However, it is now eight years since the ambitious club, which has had four coaches in the past two years, won their last league title.
Garrido, formerly coach of Villarreal, took charge in Bruges after the Belgian side sacked ex-national coach Georges Leekens following five consecutive losses.