The Rosanero are after their latest tactician to prepare them for life back in Serie B after relegation from the top flight this term.
Gattuso, who left Milan last year, stepped up as player-Coach of FC Sion in February, but after a run of just 10 points from 11 games, was replaced.
However, speculation today is that the 35-year-old is under serious consideration by President Maurizio Zamparini to take over at the Renzo Barbera for next season.
Gattuso, who is seen as favouring a 4-2-3-1 model, could reportedly be in the job by the start of June.
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