Former Leeds United boss Marcelo Bielsa has told Everton that the team doesn't have the characteristics to play his brand of football.
The Toffees are hunting for a replacement for the sacked Frank Lampard this week.
While the Daily Mail and others have reported that Bielsa is the first choice, he may not see it that way.
The source adds that while the two parties have spoken, Bielsa let Everton know he was apprehensive about taking the job.
The 67-year-old is known for his intense, high energy style of play, which the Toffees would have to work extremely hard to implement.
Ex-boss Sam Allardyce is another candidate for the post.