The Toffees lost David Moyes to Manchester United are in search of a quality gaffer to take the reins at Goodison Park.
Wigan Athletic’s Roberto Martinez appeared to have had the job sewn up but Sky Sports sources suggests that Rangnick has now entered the race.
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."