Patterson told NBC 5 that he has not spoken with Kansas State and has not accepted a job with the Big 12 school.
NBC 5 also contacted Kansas State who said they had not spoken to Patterson about the head coaching position.
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Patterson's Horned Frogs are 9-2 following Thursday night's 13-10 last-minute loss to No. 10-ranked Utah. Prior to the loss, TCU was ranked No. 11 in the country.
Kansas State fired head coach Ron Prince Wednesday and rumors have been circulating the Internet on his possible replacement.
TCU plays their final regular season game at home against Air Force on Nov. 22.