The 25-year-old only returned to his homeland in February as part of a deal which took Guilerme to Dynamo Kiev.
Kleber had spent four years in Ukraine but headed back to South America in a move which also involved Cruzeiro receiving 5million euros (£4.3m) for their man.
He has now revealed that he is attracting interest from Europe once more, with Liverpool keen to take him to England.
"I have a proposal from Liverpool for 7million euros (£6m). We are analysing [it]" said the striker on SporTV's Arena programme in Brazil.
Kleber penned a five-year contract upon his return to Belo Horizonte and it appears he would rather see out that deal than take on a new challenge in the Premier League.
"I want to stay," he added.
"If Cruzeiro offer the same amount, or we talk, I'd prefer to stay. But we haven't talked yet".
The volatile frontman, who has also attracted interest from Everton in the past, has been a revelation since returning to Brazil, netting 19 goals in as many appearances for Cruzeiro.