Costa revealed earlier this month that he has been told that he has no future at Stamford Bridge by manager Antonio Conte, despite scoring 20 times to help fire Chelsea to the Premier League title last season.
The 28-year-old is keen on a return to Atletico Madrid, but the Spanish outfit are currently serving a transfer ban which means that they are unable to sign any new players until January.
That has forced Costa to look at alternatives in Europe and beyond, but his elder brother suggested that a switch back to his home nation is not on the agenda.
"He has great affection for Atletico but right now, there is nothing (official) so we have to wait and see what happens," he told Yahoo Brazil.
"A move to Brazil? "To be honest, right now that is very difficult – many friends have called me up in the last few hours to ask me about but Diego has not said anything about this. He is a Palmeirense [fan] even though me and my father support Sao Paulo."
Costa has scored 58 times in 120 games for Chelsea, helping the club to two Premier League titles in the process.