Pereira - who has managed the likes of Porto and Fenerbache in the past - was thought the be the frontrunner for the role and he gave his thoughts on the vacancy earlier this week.
The 53-year-old - who is rated as 6/1 second favourite to be appointed with SkyBet - told Sky Sports News: “I had a few interviews - not just one.
“More than one interview with different people at the club.
“We discussed everything. I discussed with different people in the club and on the board.
“I gave them my point of view about the club and what I think about the team, because they asked me to come, Moshiri and Bill Kenwright and other people in the club.”
But it is former Chelsea boss Frank Lampard that is now 1/3 favourite to be named as successor to Benitez.
The former Derby County boss has been out of work since he was sacked by Chelsea just over a year ago.
Lampard has been linked with several clubs during that time - but he now looks to be closing in on a role at Goodison Park.
Club legend Duncan Ferguson - now 8/1 with SkyBet - is also believed to have met Moshiri on Friday and he remains in caretaker charge for the time being.
However, the former Toffees striker hinted he feels he doesn’t have the necessary experience to take control on a permanent basis.
Speaking in the aftermath of Benitez’s departure, he said: “Maybe down the line. One day I dream of becoming Everton manager.
“But of course I've not quite got that experience so my job at the moment is to take the upcoming games, steady the ship and the club will go through a process of identifying the new manager.”
Niko Kovac, Fabio Cannavaro and former Toffees manager Roberto Martinez have also been linked with the vacancy but have drifted in the betting odds.
One name to rule out is boyhood fan and former Everton striker Wayne Rooney.
He revealed he had turned down an offer of an interview from his old club on Friday morning.
He told a press conference: “Everton approached my agent and asked me to interview for the job, which I turned down.
“I believe I will be a Premier League manager and I am ready for that 100 per cent. If that comes with Everton in the future, great.
“But I have a job at Derby, which is important to me and now I'm getting ready for a game on Sunday.” They got in touch with my agent and he let the administrators know.
“It was a difficult decision. That is where we are at.”