"I want to analyse the situation," 51-year-old Hagi told reporters on Tuesday, adding that he will be replaced by his assistant Catalin Anghel, who was coach from 2009 to 2013.
"I still don't know if I'll be here in the summer," he said regarding whether he would resume his coaching duties.
Hagi, nicknamed "The Maradona of the Carpathians" and considered Romania's all-time greatest player, founded Viitorul in 2009 and still owns the club, known for nurturing young talent in the Black Sea state.
In August, Viitorul went top of the Romanian league for the first time in the club's six-year history but they have fallen away, collecting two points in their last eight games.
Viitorul's loss of form has left them in fifth spot in the table, 17 points behind leaders FC Astra.
Hagi, who won 125 caps and went to three World Cups, played for several top European clubs including Real Madrid and Barcelona. He won the UEFA Cup with Galatasaray in 2000.
(Reporting by Angel Krasimirov; Editing by Ken Ferris)
