Rutten, who joined PSV as head coach in July 2009 after spells at Twente Enschede and Schalke 04, was held responsible for the club's dismal form which included successive heavy league defeats against Twente and NAC Breda and a 4-2 defeat by Valencia in the first leg of their Europa League, last 16 tie.
PSV are fourth in the Dutch league, four points behind leaders AZ Alkmaar.
Cocu had two three-year spells at PSV and won four titles with the club. He also played for Barcelona for six years, winning the Spanish title in 1999, and won 101 caps.
PSV will host Valencia on Thursday and play fifth-place Heerenveen on Sunday in the league.
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