Carlo Ancelotti is Everton's first choice to be their new manager with the Toffees set to intensify their attempts to secure a deal for the Italian.
However, reports that the 60-year-old was on Merseyside on Monday to hold talks were wide of the mark.
Ancelotti was sacked by Napoli after taking them into the Champions League knockout stages.
A statement from Everton said the club had "held meetings with a number of candidates".
"We can confirm that thus far no contract offer has been made and no candidate has chosen to withdraw from the process," added the statement.
"While the club is keen to confirm a new permanent manager as soon as possible, the only important duty is that the right appointment is made.
"While our process continues, Duncan Ferguson will remain as caretaker manager and will take charge of the side for Wednesday night's Carabao Cup quarter-final against Leicester City."
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Everton owner Farhad Moshiri sees three-time Champions League winner Ancelotti as a big name to underline his ambitions.
It would be regarded as a major coup should he actually pull it off and it is understood talks have already taken place.
Everton will now move to set up further face-to-face discussions in a bid to persuade the Italian, who won the Premier League and FA Cup Double at Chelsea in 2010, to make a swift return to football on Merseyside.
Ancelotti is not the only option for Everton. Former manager David Moyes is also under consideration, although his name met with a negative reaction from supporters. RB Leipzig's head of sport Ralf Rangnick has also been touted as he was a candidate to succeed Moyes when he left for Manchester United in 2013.
Mikel Arteta was another with admirers among Everton's hierarchy, although it now looks more likely he will leave his role as Manchester City assistant manager to take over at Arsenal, after holding talks with the Gunners.
Duncan Ferguson, meanwhile, will continue in his role as caretaker manager for the Carabao Cup quarter-final at home to Leicester on Wednesday.
Such has been his spectacular impact on and off the pitch in getting four points from two tough league games against Chelsea and Manchester United, he is assured of a key role even if a new manager comes in.