Ireland international Robinson, who won the league, League Cup and European Cup with Liverpool in the 1983-84 season, also played for Brighton & Hove Albion and Queens Park Rangers before finishing his career with Spain's Osasuna.
Robinson stayed in Spain after his playing career and became a respected television commentator, pundit and presenter.
"Liverpool FC is deeply saddened by the passing of former player Michael Robinson, aged 61," the club said in a statement.
"With tremendous sadness we inform you of Michael's death. It leaves us with a great emptiness but also countless memories full of the same love you have shown him," his family wrote on his Twitter account.
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I met Michael a number of times when I was sports editor of the Bulletin. First thing he did was give me his mobile phone number and said if I need any advice or information to call him at any time. He was always humble and engaging and always willing to help me, who at that time was a youngster learning his way in sports journalism. Many people in the UK will not realise the importance Michael had in Spain for football commentary and analysis. I remember his television show "El dia despues" with fond memories as will many Spanish football fans. He is one of few people who transcended countries to become a household name on television in Spain. RIP Michael Robinson.