The Portuguese is in advanced negotiations with Forest about succeeding former manager Sean Dyche, who was sacked this week.
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Pereira, formerly Wolves manager, is in line to ink a deal to June, 2027.
The 57 year-old guided Wolves away from the dropzone last season, though was dismissed in November.
Pereira has also worked with Forest owner Evangelos Marinakis in the past as coach of Olympiakis.
Forest currently sit one place outside the Premier League's bottom three, three points from 18th-placed West Ham United.