"There has been contact and he was interested in the idea of playing here," Rodolfo Landim was quoted by Brazilian media as saying.
"He is a great player, without a doubt. But a lot can change before he signs with us.
"It's true that he is free (from any contract)," Landim said, adding that Flamengo officials had already met the 28-year-old player in Europe.
Sky Sport in Italy reported at the weekend the possibility of Balotelli joining Flamengo for two and a half years.
The striker, who played for Italy in Brazil during the 2013 Confederations Cup and the 2014 World Cup, has never hidden his fascination for the country's football.
Sitting in third spot in the Brazilian championship, Flamengo have been active in the transfer market recently, recruiting ex-Bayern Munich defender Rafinha and former Atletico Madrid full-back Filipe Luis.
It comes as Brazil captain Dani Alves returns home after signing a three-year deal with Sao Paulo.
Spanish international Juanfran, another former Atletico player, is also joining the side, the club said Saturday.