Flamengo vice president Marcos Braz and football director Bruno Spindel traveled to Europe on Monday night in a bid to bring the 29-year-old to the Maracana, the Globo newspaper reported.
It added that Balotelli had given a "green light" for negotiations and that Flamengo hoped to secure the forward in time to register him for the Copa Libertadores quarter-finals, which start next week, reports Xinhua news agency.
Balotelli, whose career has included spells at Inter Milan, Manchester City, Liverpool and AC Milan, is a free agent after parting ways with Marseille in June.
His arrival would follow a series of high profile signings by Flamengo this year, including former Bayern Munich right-back Rafinha and ex-Atletico Madrid defender Filipe Luis. The club also secured Inter Milan striker Gabriel Barbosa on loan in January.
Flamengo manager Jorge Jesus has made no secret of his desire to sign a central striker and last week he told reporters that Balotelli was on his wish-list.
The Rio outfit are currently third in the 20-team Brazilian Serie A standings, five points behind leaders Santos after 13 rounds. Last Wednesday, Flamengo advanced to the last eight of the Copa Libertadores South America's top club competition by defeating Ecuador's Emelec on penalties in the second leg of their last 16 clash.
They will meet Brazilian rivals Internacional in the quarter-finals over two legs on August 21 and 28.
( With inputs from IANS )