The Portuguese manager had been hot favourite to stroll into the role, but protests from Everton fans have led to the bigwigs at Goodison having second thoughts.
This has opened the door for Lampard again, spooking the bookies into slashing his price and making him odds-on favourite for the role.
Surprisingly Pereira appeared on live television to discuss the job and admitted he was hurt by fan opposition to his potential appointment, but it has not put him off wanting the job.
Pereira has already had two interviews with Everton owner Farhad Moshiri but said he did not know what the outcome was and the "decision was the club's".
Reports the former Porto and Fenerbahce coach was edging closer to replacing Rafael Benitez led to the message 'Pereira out, Lampard in' being painted on a wall at Goodison Park.
Asked whether the graffiti hurt him, he told Sky Sports News: "Of course. This is the first time in my career I have seen this kind of thing, I've never had these comments about me.
"I think these critics are not directed at me. It is the environment now as the club is not in a good position and the supporters are passionate - and this passion is the power of the club.
"They don't know me, my work or me as a person or my CV. I don't take it as a personal attack. I work in a lot of countries, different clubs, at different levels, and we got several titles but before you start work you don't know the person and you cannot judge.
"But I understand the feelings of the supporters because, in the last few years, the club didn't get good results and it is normal they are not happy."
On Monday evening a number of supporters congregated outside the Liver Building - where Everton's commercial offices are based in the city - and another protest was planned for Tuesday night at the Dixie Dean statue outside Goodison Park.
Fans were due to voice their objections to Pereira, agent Kia Joorabchian - reportedly advising Moshiri - and the continued stay of long-standing chairman Bill Kenwright.
The turmoil at the club has not deterred Pereira, however, who added: "This is something I cannot control."
Pereira, who won back-to-back titles with Porto as well as a championship in Greece with Olympiacos but also got relegated with 1860 Munich, continued: "What I want to tell you is all of my career I worked under pressure, I worked at clubs where we cannot draw one game.
"For a manager the pressure must be the source to be at the best level. The pressure about the decision is something I cannot control.
"What I felt in the meetings was they were very positive with the interviews. I think they were enthusiastic about what I proposed to them.
"I did my work and now the decision is not controlled by me. They have other candidates and this is a time for decisions. I just wait for the decision, be calm. I will move forward with my life and if they want me they must call me.
"Otherwise it is 'Thank you very much and it was a pleasure to be here'."