Fearnley-Whittingstall wants Tesco to force its suppliers to improve conditions for poultry production by moving to Freedom Foods standards and is tabling a proposal for the retailer's annual general meeting.
However, Tesco said the proposal has been submitted late and have told the chef he must bear the cost of sending the papers to investors, a total of £86,000.
Fearnley-Whittingstall is reported to be hoping to raise the money through his chickenout.tv website by holding an auction with a number of prizes, but he has called on Tesco to drop its demands.
"I think Tesco should waive this bill, which it is at its discretion to do. At the same time, it's clear that it doesn't really want this resolution," he told the Independent on Sunday.
However Tesco said it could not expect its shareholders to pay for the cost of the documents to be produced and distributed, but said it had extended the deadline for Fearnley-Whittingstall to pay the bill to Wednesday.