Everton have put Duncan Ferguson in as caretaker boss as they look for a permanent successor to Rafael Benitez.
Ferguson’s Everton were beaten by Aston Villa at the weekend and relegation worries now loom large in the corridors at Goodison Park, with the club just four points above the drop zone.
The club are looking to get a permanent boss in and have held interviews with a number of contenders.
Portuguese tactician Pereira, 53, held talks with Everton in recent days and impressed the Premier League side.
It is suggested he is now emerging as a serious contender to take charge.
Club owner Farhad Moshiri wants to make an innovative appointment, bringing in someone who can develop the Toffees with fresh ideas.
Pereira, who counts FC Porto amongst his former clubs, has been interviewed by Everton twice previously, but on both occasions the Toffees chose not to appoint him.
His last post was at Turkish giants Fenerbahce, who he joined in July 2021 and where he was sacked in December.