The fire engulfed a dormitory at Ninho de Urubu, the youth team training centre of Flamengo in Rio De Janeiro, at around 5am local time on Friday morning.
The SporTV channel said the victims included six players and four members of staff.
Passion for soccer runs deep in Brazil, and as news of the tragedy spread, numerous world's best players and top officials expressed condolences.
One of them was identified as Christian Esmerio, a 15-year-old goalkeeper.
"We are distraught", Flamengo president Rodolfo Landim told reporters, according to The Associated Press. Many players, particularly those who live outside of Rio de Janeiro, stay at the facilities while training.
"I still can't believe it but praying for all". The fire was reportedly controlled around 7:20 a.m.
Brazilian star forward and Paris Saint-Germain player Neymar posted the club's crest on Instagram, writing: "My sentiments".
As news of the fire broke, several teams and players expressed their condolences on Twitter.
"I'm very sad", said 16-year old Augusto Mateus, who turned up wearing a red Flamengo shirt.
The rains led Flamengo to close parts of its social club and cancel regular training sessions it organises for children.
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 Ninho do Urubu, or Vulture's Nest is so called because the club's symbol is a vulture.
Brazil football legend Pelé described the club as "a place where young people pursue their dreams".
The training camp is in an area of western Rio that was hit by a huge storm Wednesday night.
Law enforcement officials in Brazil's second largest city say that at least 11 suspected drug traffickers were killed in a shootout with police in a slum located in the bohemian Santa Teresa neighbourhood.
Thirteen of the 26 players in the dormitory were able to escape the fire without any significant injuries; three others were rushed to the hospital and 10 did not survive.