The comedian had the 13ft model built for a recent Walkers crisps advert, and it is now going up for auction.
However, since Carr's recent tax avoidance scandal, the owners are concerned that only Carr may bid the reserve price of £3,000.
Jimmy Carr recently apologised for his involvement in the scheme, which saw his tax sheltered in Jersey.
Yard owners Paul Johnson and Dale Sumner paid £2,000 for the replica head last year in Preston, Lancashire, reports The Sun.
They are hoping that Carr may bid on the item as a means to improve his public perception.
Jonathan Isaby of the TaxPayers' Alliance said: "Given the press Jimmy Carr's had, I'm not sure who's going to want to buy this replica. Perhaps he ought to make an offer himself."
Carr's post-tax avoidance episode of 8 Out of 10 Cats saw a big ratings increase last week.