"There is a very good possibility that I will be named Red Star's coach by the end of this week," Prosinecki, who won the 1991 European Cup with Red Star, told Reuters.
"I have spoken to the club officials and I will come to Belgrade on Thursday for final talks which should result in my appointment," he said.
Red Star president Vladan Lukic told local reporters that the decision was up to the club's executive board.
"The executive board will decide on Thursday who the new coach will be. As far as I am concerned Prosinecki is a Red Star legend and a great character," Lukic said.
Red Star on Tuesday parted company with Aleksandar Kristic, who took over in August after the team made an 18th successive early exit from Europe and came under pressure in October following a 1-0 derby defeat by champions Partizan Belgrade.
Partizan have won three league titles in a row and top the 16-team first division at the winter break, five points ahead of second-placed Red Star.
Prosinecki, who reached the 1998 World Cup semi-finals with Croatia, has worked as an assistant to national team coach Slaven Bilic since 2006 after ending his playing career at Croatian top-flight side NK Zagreb in 2004.
He scored 10 goals in 55 appearances for Real Madrid between 1991 and 1994 and had a brief spell with Barcelona in 1995-96.
