Former Arsenal boss Unai Emery was approached about the Everton job, Sky Sports News understands.
An informal meeting was held in London and it is thought Emery wants more time to think about his next move following his dismissal as Arsenal head coach.
Emery is keen to continue improving his English as he sees England, as well as Spain and Italy, as viable options for his next job.
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The Spanish coach is taking time out after Arsenal, but he does not want to wait too long and is already thinking about his next challenge.
Everton are on the hunt for a new manager after they parted ways with Marco Silva last week, with Shanghai SIPG boss Vitor Pereira believed to top the board's list, Sky Sports News understands.
Chairman Bill Kenwright and majority shareholder Farhad Moshiri have drawn up a four-man shortlist, including Napoli boss Carlo Ancelotti.
It has been confirmed to Sky Sports News Emery was desperate to sign Wilfried Zaha in the summer, as reported during the last window.
Emery also wanted to sign a central defender, and was keen on Harry Maguire - but he proved too expensive.
How to follow the January transfer window
Sky Sports will bring you the very latest news from the January transfer market with the return of three shows.
Start your day with Good Morning Transfers at 9am as our team of reporters bring you the latest news and insight. Transfer Talk then follows at midday delivering analysis of the biggest stories. Then join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
Meanwhile, the Transfer Talk podcast will also be back at the turn of the year with more expert analysis from here and across the continent.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.