Sky sources understand that Everton have spoken to former Schalke coach Ralf Rangnick about their vacant manager's position.
Everton are looking for a replacement for David Moyes, who has left to join Manchester United, and Roberto Martinez is an odds-on favourite to take the post.
Vitor Pereira of Porto is also believed to be in the mix, and 54-year-old Rangnick has now emerged as a contender in what is believed to be a three-man shortlist.
Rangnick has managed several German sides but stepped down as Schalke boss in September 2011, citing exhaustion.
Sky Sports reporter Vinny O'Connor said on Thursday evening: "There have been several rumours about the next Everton manager.
"And one of the names who has constantly cropped up is Ralf Rangnick, the former Schalke coach. He enjoyed success with them in the Bundesliga, but left in 2011.
"It is my understanding that there has been a meeting between Everton and Ralf Rangnick, and he is one of the contenders for the vacant manager's job.
"We know (Everton chairman) Bill Kenwright met with Roberto Martinez yesterday, and we also know from sources at Wigan that they want an answer relatively quickly as to what's going on regarding Robert Martinez, because they want to find a replacement should he be going to Everton.
"So, we know Kenwright met with Martinez, we know he met with Porto coach Vitor Pereira last week, and now we also know that Ralf Rangnick is another name in the frame."