Of the ten, four are Flamengo youth team players, two are young boys on trial, and four are club employees.
The fire broke out on Friday at Ninho do Urubu, a state-of-the-art training centre that was expanded and opened only two months ago.
The cause was not immediately known, but local newspaper Extra said witnesses alleged the fire started in the air conditioning system.
He did not take questions from reporters who also were outside the complex but added: "The most important thing right now is to minimise the suffering of these families".
Local reports stated 10 people were feared to have died, while fire department chief Douglas Henaut confirmed the incident occurred at the lodgings.
Local media reported that the fire happened in a dorm where youth players sleep. The ages of the injured were 14, 15 and 16, according to a fire official who spoke on condition of anonymity because of agency rules.
Brazil's Pele, widely regarded as the best player to ever live, said: "It's a very sad day for Brazilian football". The fire was reportedly controlled around 7:20 a.m.
Like many clubs who sign youngsters from across the country, the facility has accommodation for teenagers, although it was unclear exactly how many players were among the dead.
Felipe Bornier, the Rio state sports secretary, told journalists that "we must absolutely give all the support necessary to the victims' loved ones because a lot of them aren't from Rio".
The Ninho de Urubu ("Vulture's Nest" - so named because the symbol of the club is a vulture) centre underwent a major expansion past year, with the club spending 23m reals (£4.8m, $6.2m), Reuters news agency reports.
Teenage Real Madrid forward Vinicius Junior, who came up through the youth ranks at Flamengo before signing with the European Champions in 2017 for 45 million euros ($51 million), posted a message on Twitter asking people to pray for the victims.
Youth league teams also train at the facility, known as Ninho do Urubu, which means "the vulture's nest".
Real Madrid forward Vinicius Junior, who joined the club from Flamengo previous year, said: "Just remembering the nights and days I spent at the training center, it gives me goosebumps".
The fire follows days of heavy rains that hit the city and claimed at least six lives.
"What a shock getting this news here on the other side of the world", Brazilian midfielder Zico wrote on Instagram.
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