Ancelotti is on the verge of moving away from Everton this summer with his return to Real Madrid set to be sealed imminently.
Everton were not planning to look for a new manager this summer but have now been forced into starting the process of identifying the right man.
It has been claimed Everton are now in the process of drawing up a shortlist of names they are willing to pursue in order to bring in Ancelotti’s replacement.
And it has been suggested that Rangers boss Gerrard is one of the names who is on Everton’s radar this summer.
The former England midfielder has proved himself north of the border by taking Rangers back to the summit of Scottish football.
However, Gerrard is still only an option and he is not thought to be considering leaving the Gers yet.
And being a boyhood Liverpool fan and legend at Anfield, he is also unlikely to consider the Everton job.
Former Liverpool boss Rafael Benitez, ex-Toffees manager David Moyes, Paulo Fonseca, Erik ten Hag and Roberto Martinez are also said to be in the frame.