According to The Daily Telegraph, bank notes in prime condition will be sold for hundreds of pounds.
The notes are unique in that they have low serial numbers and have not been in general circulation.
It is reported that one £50 note will be auctioned from prices starting at £300 to £400.
The Bank of England began to issue bills with a new official signature last week.
Bank notes signed by Chief Cashier Chris Salmon entered circulation on September 12, while notes signed by former Chief Cashier Andrew Bailey will be gradually removed from use.