The Brazilian striker ruled out moving to Anfield on Sunday, but performed a u-turn by insisting negotiations were taking place and, according to local reports, the Reds would pay 7 million euros (¦pound;6million) for his services.
When SporTV channel asked him whether he was going to play for the Merseysiders in the Barclays Premier League, Kleber said: "I don't know yet. They are talking."
The player, however, would like to stay in his homeland.
"Cruzeiro have been made an offer," he added. "I've always said I wanted to play in Brazil and make history here because I know it is possible.
"But I also know the team need to transfer players as they have commitments. We'll see."
The 25-year-old, nicknamed 'Gladiator', was signed by the Belo Horizonte side from Dynamo Kiev when the Ukrainians paid five million euros plus Kleber for Guilherme.
"I want to stay, but if Cruzeiro can afford it," Kleber said.