They claim Celtic are looking to pay 300,000 euros to loan the player from January to June with a 2.5m euro option to sign permanently.
Cruzeiro, however, are looking for 1m euros for the loan and a 4m euro option.
Bruno is also looking to release himself from his contract after filing a lawsuit against the club for unpaid wages.
The Cruzeiro statement read: “Cruzeiro explains it has not received any official proposal from Celtic for defender Fabricio Bruno.
“The player’s agent Fabio Mello was at Toca da Raposa 2 [club training centre] in the company of Bruno this week and met with the club’s board, represented by directors Marcelo Djian, Benecy Queiroz, Valdir Barbosa and football vice president Marcio Rodrigues.
“Mello reported he met with Scottish club officials in London, England and was authorised to make a proposal from January to June 2020 with Celtic paying 300,000 euros for the loan and 2.5m euros if Bruno was approved.
“Cruzeiro did not accept and countered 1m euros for the loan and 4m euros if the player was approved.
“Director Djian even said if Bruno did not stay with Celtic he would return undervalued and Cruzeiro would only receive 300,000 euros, a very small amount.
“The agent of the defender said the amount requested by Cruzeiro was a little high but he would work to increase the values of the loan and sale.
“Mello also said he would be travelling on December 26 to London and invited Djian to join him in the negotiation.
“Cruzeiro never ended the negotiation but was surprised by agent Mello who later called Djian and Queiroz apologising and warning the case would be brought to justice by Bruno.”