All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If these properties are owned by the bank in a lawful way, then it is permissible to purchase them whether these banks are Islamic banks or they deal with Riba (interest and usury), because it is permissible to deal in permissible transactions with a person who deals with Riba. Auction sale is permissible on the following conditions:
1- There should be no intention of harming anyone.
2- The person increasing the price should really have the intention of buying, otherwise he is just increasing the price for the person who wants to buy, and this is forbidden.
However, if these properties are owned by the bank by an non-Islamic and impermissible method, like owning it in return for interests which the owner of the property has to pay, and then there was a court order for selling the property by force in order to pay the interests, then in this case it is not permissible to buy it as it takes the ruling of buying something stolen and the like. For more details please refer to Fatwa 84222.