"The money being offered is nowhere near the kind of money that Bruno will earn as the holder of this prestigious world title," said Frank Warren, who in association with Don King has a promotional contract with Bruno.
If there is no acceptance - and the mandatory period does not begin until 24 September - Panos Eliades, Lewis' backer, has asked the WBC president, Jose Sulaiman, to call for purse bids by 9 October.
Lewis won the right to fight for his former title by stopping Lionel Butler in an official final eliminator in Sacramento in May, but Mike Tyson's release and immediate elevation to No 1 in the WBC rankings threatens to complicate the issue.
First, though, Lewis has to overcome the dangerous Tommy Morrison in a 12-round non-title bout at the Atlantic City Convention Center on 7 October.
The battle in the United States for which fight will be staged on 4 November -Tyson v Mathis or Holyfield v Bowe - swung Tyson's way when King struck a deal to have the contest shown on national television and not pay-per- view.