Pereira, 57, became Forest’s fourth permanent manager of the season when he replaced Sean Dyche in February.
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He has since taken them clear of the relegation zone and to a Europa League semi-final, although they were knocked out by Aston Villa.
According to The Athletic’s David Ornstein, the club’s hierarchy have been impressed with Pereira and are readying a long-term contract offer.
There had been speculation of another managerial change at the City Ground, with owner Evangelos Marinakis a long-term admirer of Fulham’s Marco Silva.
Pereira signed an 18-month contract when he joined, and although he has another year on it, the club are keen to create stability and extend his stay.