Felix is a talented midfielder who has played for Chelsea in the past, and Flamengo's coach, Filipe Luis, is a former Chelsea player as well.
Flamengo wants Felix to lead their team's attack ahead of the Club World Cup, which is a prestigious international tournament.
The club has made contact with Felix's representatives to discuss a possible loan deal with an option to buy him permanently at the end of the season in December.
Felix is currently without a regular spot in London or Milan, but he still hopes to succeed in European football before considering a move to South America.