The player had announced on Monday that he was the subject of a 7million euros (£6m) offer from Liverpool.
That story has since been big news in South America, with the 25-year-old's future the hottest topic on the football-mad continent.
However, his current employers have reported that no such bid has been lodged, and claim they would not be prepared to do business for anything less than 15million euros (£13m).
Kleber is keen for the issue to be laid to rest, but has admitted that he would be happy to strike a deal with a European club this summer should an opportunity arise.
"I don't want to speak about this anymore, it's getting annoying" said the former Dynamo Kiev frontman.
"Quite soon, if we start playing badly, the fans will start to say it's because I want out.
"If there was an offer, it would be good for me and Cruzeiro.
"My agent (Pepe) and Zeze (Perrella, club president) are going to sit down and sought this out."