Genoa lost 5-4 at Inter Milan on Sunday in Andrea Stramaccioni's first game in charge of the hosts and have slipped down to 16th in the table, six points above the drop zone with eight games left.
Marino replaced Malesani in December but results got worse for a side hoping to challenge for Europa League spots at the beginning of the season.
Italian teams often bring back previously sacked coaches because they remain on the payroll until their deals are paid up and are therefore cheaper to employ than other candidates.
The pool of potential bosses is also limited by the fact that coaches are only allowed to manage one Serie A team in a season under league rules.
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