Ljupko Petrovic
Daily Sportski zurnal said Petrovic had reached agreement with Red Star director Dragan Dzajic, and was awaiting formal approval by the club's managing board.
"It's a foregone conclusion and Petrovic will be officially appointed as the new manager on Monday," the daily quoted Dzajic as saying.
Petrovic has been lined up to replace Slavoljub Muslin, who resigned last month after winning the domestic double with the team.
Media reports suggested there had been a rift between Dzajic and Muslin over the club's transfer policy, although Dzajic said the coach had resigned in spite of frantic efforts by the club to keep him at the helm.
Petrovic has had two spells with Red Star, during which he won the European Cup in 1991 and three national championships.
He won the Bulgarian Cup with first division side Litex Lovech last season.