Vitor Pereira won 14 of his 38 games in charge of Wolves
The Premier League club sacked Sean Dyche shortly after being held to a goalless draw by bottom club Wolves on Wednesday, leaving them three points above the relegation zone with 12 games remaining.
BBC Sport earlier reported Forest had opened talks with Pereira and those discussions are understood to have progressed with an agreement now described as close.
The 57-year-old quickly emerged as the preferred option to replace Dyche, having worked previously under Forest owner Evangelos Marinakis at Greek club Olympiacos.
Pereira was credited for keeping Wolves in the Premier League last season having joined midway through the campaign, but he was sacked in November with the club on two points from 10 matches.
The Portuguese is in line to become Forest's fourth manager of the season following Nuno Espirito Santo, Ange Postecoglou and Dyche.
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