Nottingham Forest sounded out Lorenzi ahead of a summer in which significant structural change is expected at the City Ground.
Global head of football Edu, whose arrival was seen as a coup barely 12 months ago, is expected to leave with his broad remit across owner Evangelos Marinakis's club portfolio — which includes Olympiacos and Rio Ave — never having fully functioned.
Head of football development Craig Mulholland is also set to depart to become the Scottish Football Association's new chief football officer.
Lorenzi leaves Brest having built one of the most admired scouting operations in French football, operating on a minimal budget and discovering players sold on at significant profits.
His decision to leave was influenced by the strain of that tight financial environment and frustration at public criticism of his transfer business by head coach Éric Roy last summer.
Crystal Palace, Marseille and Saint-Étienne were also credited with interest. Nice moved fastest and have agreed terms, according to Foot Mercato.
Forest have been through four managers this season — Nuno Espírito Santo, Ange Postecoglou, Sean Dyche and now Vítor Pereira — but remain five points clear of the relegation zone with four games remaining and are in the Europa League semi-finals against Aston Villa.