Adriano was due to fly back to Italy on Thursday after Brazil's World Cup qualifier against Peru in Porto Alegre, where he was an unused substitute.
The Brazilian media has been rife with speculation about what has happened to the player but Inter coach Jose Mourinho has already said he did not consider it to be a case of indiscipline.
"It's not a family problem," Gilmar Rinaldi told Brazilian media, according to Globo television's website. "It's something very personal, which could happen to anyone, but it's a private thing and that's why I can't say what it is."
Once one of the world's most fearsome strikers, Adriano has struggled with fitness and alcohol problems since the 2006 World Cup and shown only small doses of his previous form since then.
Rinaldi confirmed that Adriano had been in the Vila Cruzeiro shanty-town where he was raised visiting friends.
"I don't have the right to ask Adriano not to go to the Vila Cruzeiro because it's where his family lives, where he grew up," Rinaldi said.
"The price you pay for being someone who is well-known and for coming from where he came from is very high."
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