"As much as we tried to get inside and find people still alive that wasn't (possible). we only found bodies inside".
The blaze engulfed a dormitory at the youth team center where the players were sleeping.
The cause of the fire is now unknown.
"We are distraught", Flamengo President Rodolfo Landim said outside the complex, where friends, fans and neighbors gathered, some forming a circle to pray. Overhead images captured by an Associated Press drone showed a smoky, charred area of the complex.
"This is certainly the worst tragedy that this club has gone through in our 123 years with the loss of these 10 people".
Globo TV broadcast aerial footage of the fire, which it said had been brought under control after it burned for two hours.
It was not known if any players were hurt in the blaze, although the Rio de Janeiro-based club has accommodation for teenage players at the ground.
The fire brigade said in a statement that the center was "in the process of" meeting fire safety standards but did not yet have a certificate of approval.
The Brazilian news channel identified at least six of the dead as youth players.
However, numerous lodgings have a reputation for poor health and hygiene standards.
Among the most famous players to come through the club are Ronaldinho and Zico, former stars on Brazil's national team; top goalscorer Adriano, who rose to fame at Inter Milan; and current Real Madrid star Vinicius Jr, who not long ago was living in the building destroyed by the fire. Many, particularly those who live outside of Rio de Janeiro, stay at the facilities while training.
After years of financial difficulties, Flamengo last year spent $6.2 million United States to expand the Ninho do Urubu training ground.
Youth league teams also train at the facility, known as Ninho do Urubu.
The fire follows days of heavy rains that hit the city and claimed at least six lives.
Messages to Flamengo officials were not immediately answered.
Several of the club's best-known young talents trained there, including midfielder Lucas Paqueta, who made his debut for AC Milan in January, and Vinicius Junior, who joined Real Madrid past year.