In a primary High Court hearing on Thursday, the company's lawyers said the singer has run up costs of more than £500,000.
Sir Cliff filed a lawsuit against the BBC and South Yorkshire Police due to the 2014 police raid in his home. The raid was in connection with sexual assault allegations, which he was later cleared of.
The singer claims the raid was an invasion of his privacy.
If Sir Cliff wins the legal battle, the BBC could be required to pay some or all of his lawyers costs.
