Everton are seeking a new manager after Sunday's sacking of Rafa Benitez.
Italian transfer expert Nicolo Schira reports Gattuso is being discussed at Everton amid talk of a deal being close with Belgium coach Roberto Martinez about a return.
Gattuso came close to joining Tottenham last summer and remains a free agent after leaving Napoli at the end of last season.
The Italian has past playing experience in the UK with Rangers.
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