The Toffees were hamstrung by Financial Fair Play regulation during the last transfer window, which prevented them from make any huge investments in player recruitment.
Everton spent under £2m in the summer with the majority of their new players coming in as free transfers, but they have since made more space on the books by offloading high earner James Rodriguez to Qatar outfit Al-Rayyan.
The Merseyside giants were linked with interest in Napoli skipper Insigne during the summer transfer window but no move materialised.
But according to Italian daily Tuttosport, Everton are still keen on Insigne and are looking to enter negotiations with him when the winter transfer window swings open.
Insigne has entered the final year of his contract at the Stadio Diego Armando Maradona and is allowed to sign a pre-contract agreement with potential suitors.
However, Everton are not the only club interested in Insigne’s services as Italian champions Inter are keeping a close eye on his situation at Napoli, while French giants Paris Saint-Germain are also among his admirers.
New Everton boss Rafael Benitez worked with Insigne during their spell together at Napoli and it remains to be seen whether the Toffees will make any solid moves for him in January.
