Costa was told in the summer by Blues boss Antonio Conte that he has no future with the Premier League champions, and since then the Spanish international has remained in exile in his hometown in Brazil.
"The guy is big trouble and I know he has done well for them. But he looks a bit of a balloon, so they should get rid of him and get players in that want to be there," Keane told ITV Sport.
The 28-year-old striker was keen on a move back to his former club Atletico Madrid, but a transfer ban means that the Spanish outfit are unable to register new players until January.
Costa scored 20 league goals and registered eight assists for Chelsea in the 2016-17 season as the West London club claimed their fourth Premier League title of the Roman Abramovich era.
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