Imran said White had asked him and his wife, Jemima, ten days before her death if the couple be the girl's guardians.
"I and my wife Jemima accepted her request and decided to take Tyrian into our guardianship, although Tyrian would live in America," Imran, who heads the Pakistan Tehrik-e-Insaf party, was quoted as saying in the Daily Times.
Imran in the past has denied that he was the father of the 12-year-old, but went to New York after learning of the death of White.
He had flown to Los Angeles after multi-millionaire mother White collapsed, having apparently suffered a heart attack near her home in home in Beverly Hills.
He said White was friend of Jemima and her parents for a long time.