Pereira looked set to sign on as the First team manager after impressing in his interview and is still under consideration.
However, the reaction to his proposed appointment has been less than ideal by Everton fans.
The Portuguese manager orchestrated an interview in which he tried to explain his plans should he be appointed, but it did little to improve his standing amongst Everton fans.
In the wake of this, former Chelsea manager Frank Lampard is rumoured to be the new favourite to take over the vacant role.
Lampard finished fourth and reached the FA Cup final in his one full season at Chelsea.
Since sacking Rafael Benitez, Farhad Moshiri and Everton have appeared to lack a plan for his succession.
The Toffees have been linked with former manager Roberto Martinez, Wayne Rooney, Roy Hodgson and Vitor Pereria.
The protests after the team's loss to Aston Villa have continued into this week as hundreds of fans gathered at the stadium.
Everton has slumped towards the relegation zone after one win in 14 league games has left them four points off the bottom three.