Flamengo, the alma mater of players such as Zico, Junior and Leonardo, is one of the best-supported clubs in Brazil and is famous around the world.
The cause of the fire was not known, but Claudio Castro, vice governor of the state of Rio de Janeiro, said authorities were looking at the possibility of a short circuit in an air conditioning unit.
Apart from the 10 people reported to have lost their lives in the fire disaster, there are many persons who sustained serious injuries and are being treated in the hospital.
Like many professional clubs in soccer-crazed Brazil, Flamengo has a youth development program for promising young players in their early teens.
The club took to Twitter to announce that it "is in mourning" over the tragic incident.
Globo TV broadcast aerial footage of the fire, which it said had been brought under control after it burned for two hours.
In addition, Flamengo's match with their rivals Fluminense, previously scheduled to take place on Saturday, has been postponed to February 14 in the wake of the events. "I just spoke to Caix Suarez and he is alive", said Rodrigues, adding that the youth told him he ran when he saw the flames.
Vinicius Junior, the teenage Real Madrid forward who trained at the facility before joining for the Spanish giants past year, tweeted his condolences.
None of the victims has been identified but players aged between 14 and 17 are known to have used the dormitory.
Flamengo president Rodolfo Landim called it "the biggest tragedy in Flamengo's 123-year history" but gave no details about the players involved.
The fire broke out at 5 am in the Vargem Grande district of Rio in a modern facility where the top-flight professional Flamengo squad also trains, the news website G1 said.
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"I'm very sad", said 16-year old Augusto Mateus, who turned up wearing a red Flamengo shirt.
"As a fan and sportsman I stand in solidarity with the families, the club and the Red-and-Black nation", General Hamilton Mourao wrote on twitter.
"For poor kids, many see it as the only path", he said.
After years of financial difficulties, Flamengo last year spent $6.2 million USA to expand the Ninho do Urubu training ground.