"Finding a forever home for a tiger is not easy", she said.
"There was no concern about the tiger getting out of the cage", Cottingham said by telephone on Tuesday.
Police say the animal was being kept in a cage that was not large or sturdy enough for its size with several packages of meat nearby, according to KTRK-TV.
After a neighbor contacted 311 anonymously, police and BARC were alerted to a report of a tiger inside a southeast Houston home.
But once they arrived, police found a caged tiger in the home's garage, according to KTRK.
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The tiger was saved Monday by the House Police Department's animal cruelty unit.
Some tigers are smuggled into the United States from Mexico, and there are small pockets of breeding facilities across the country.
It is now being transferred to a sanctuary elsewhere in Texas - although the exact location has not been publicly disclosed.
It's legal to own a tiger in Texas if the owner has a wild game permit but it's illegal to have one in Houston and Tyson's owner, if found, could face a hefty fine. "More often than not it gets big, it gets expensive, it gets unsafe, and they end up turning the animal in or abandoning it". Houston police are investigating who may have owned the animal.
"This is not the first tiger that has been picked up by BARC", Cottingham said. "Malayan tigers surviving on the Malay Peninsula are critically endangered with an estimated population of 300 remaining in the wild".