Big Cat Public Safety Act This act revises requirements governing the trade of big cats (i.e., species of lion, tiger, leopard, cheetah, jaguar, or cougar or any hybrid of such species) under the Lacey Act to limit the possession, breeding, and exhibition of big cats. The Lacey Act prohibits any person from importing, exporting, buying, selling, transporting, receiving, or acquiring big cats across state lines or the U.S. border. However, some exemptions are provided for certain entities, such as universities and wildlife sanctuaries. (Sec. 3) The act expands the Lacey Act prohibitions to include a prohibition on possessing or breeding big cats. Breeding means facilitating propagation or reproduction (whether intentionally or negligently), or failing to prevent propagation or reproduction. Owners of big cats that were born before this act's enactment may keep their big cats, but the owners must register them with the U.S. Fish and Wildlife Service. The act modifies the list of entities that are exempt from prohibitions to export, buy, sell, transport, receive, acquire, possess, or breed big cats. The modified list includes exemptions for entities or facilities exhibiting animals to the public if they (1) hold a Class C license in good standing under the Animal Welfare Act, and (2) do not allow individuals to come into direct physical contact with big cats. However, direct contact is allowed if the individual is a trained professional, a veterinarian, or directly supporting conservation programs that do not involve commercial activities and meet other specified restrictions. (Sec. 4) A person who knowingly violates the act must be fined not more than $20,000, or imprisoned for no more than five years, or both. The act considers each violation to be a separate offense. The offense must be deemed to have been committed not only in the district where the violation first occurred, but also in any district in which the defendant may have taken or been in possession of the prohibited wildlife species. (Sec. 5) The act extends forfeiture provisions to fish, wildlife, or plants that are bred or possessed; thus, big cats bred or possessed in violation of the act are subject to forfeiture. (Sec. 6) The Department of the Interior must issue regulations to implement this act.