Braga coach Paulo Fonseca has been linked with the Everton job but he remains some way down the list of candidates.
Reports claim the Blues have targeted Fonseca as a possible successor to Roberto Martinez at Goodison Park after being impressed with his work in Portugal.
Fonseca led Braga to victory in the Portuguese Cup against Porto last weekend and also oversaw a fourth-placed finish in the top flight to seal Europa League qualification.
The 43-year-old, who previously guided minnows Pacos Ferreira to a surprise third-place finish in the Primeira Liga in 2013 and is regarded as one of the brightest young coaches in Europe.
Fonseca is still regarded as an outsider for the job with Ajax boss Frank de Boer, Southampton’s Ronald Koeman and Manuel Pellegrini among the leading candidates, while former boss David Moyes is also in the frame.
One man who claimed he was on Everton’s shortlist of managers was Lucien Favre but the former Borussia Monchengladbach chief has taken over at Nice after claiming he didn’t want to “wait any more” for the Blues to get in touch.
Favre said: “I know that I was on Everton’s shortlist, but I didn’t want to wait any more.”