Everton sacked Rafael Benitez earlier in January after a dismal run of one win in 13 league games left the Toffees six points above the relegation zone.
That cushion has now been reduced to four points after Everton lost to Aston Villa on Sunday (AEDT), with Duncan Ferguson having taken interim charge.
A host of names have been linked with the job, though all with vastly different profiles. Former Toffees boss Roberto Martinez, sacked in 2016, was an initial candidate, but the Belgian FA rebuffed Everton's approach.
Fabio Cannavaro is also said to have been interviewed, similarly Frank Lampard. Wayne Rooney, meanwhile, confirmed last Friday that no approach had yet been made to Derby County's administrators.
However, widespread reports on Monday claimed that Pereira was the favoured choice of owner Farhad Moshiri, whose running of the club has come under scrutiny from fans.
Those reports were met with some outcry, with a photo spread via social media on Tuesday showing graffiti at Goodison Park reading: "Pereira out. Lampard in."
With suggestions on Wednesday that Everton were still weighing up options, Pereira – who was dismissed from a second spell in charge of Fenerbahce in December – took the somewhat surprising decision to speak to Sky Sports.
"The club asked me to come for a meeting. I had a few interviews, not just one, with different people at the club, the board. We discussed everything, and I gave them my point of view about the club, the team," Pereira explained.
"I think they were enthusiastic to what I proposed. An intense game, pressing, possession. We need to give confidence to the players, to the team and the fantastic supporters. This is what I proposed to them. What I felt in the meetings was that they were positive."
Asked if he had been informed whether he would be getting the job, Pereira said: "They have other candidates and this is a time for decisions.
"No, [they have not told me]. Just to wait for the decision, be calm, and they are grateful for the interviews, that's all.
"What I want to tell you is that all of my career, I worked under pressure. About the decision? It's something I can't control.
"I built my career with passion, organisation, competence. This is what I can offer to the club. I give 100 per cent of me, football for me is 24 hours. This is my life, my passion.
"I will move forward with my life. If they want me, they must call me. That's all."
In response to the graffiti, Pereira said: "This is the first time in my career that I see this kind of thing. My CV speaks for itself. The club is not in a good position and the supporters have passion, this passion is the power of this club.
"[Critics] don't know me very well, they don’t know my work, know me as a person. I worked in a lot of countries, different clubs, different levels, got several titles.
"I don't take this as a personal attack."
Pereira has won four league titles across spells in charge of Porto, Olympiacos and Shanghai SIPG.