Michael Lohan admitted he had an affair with Kristi Kaufmann, a Texas woman, in the mid-1990s while he was separated from his wife, Lindsay's mother, Dina.
Kaufmann told OK! magazine Michael knew about their 13-year-old daughter, Ashley, but has failed to support her.
"We were in love," Kaufmann told OK!. "One morning, he told me to pack my things -- we were going to run off together. I waited, but he never showed up."
The New York Daily News said Michael Lohan has denied he ended his relationship with Kaufmann that way and insisted he only recently found out about Ashley.
He also told the Daily News he took a DNA test Monday morning to see if he was actually the girl's father.
"I'll have the result within two weeks, and I'll clear this matter up," he told the newspaper. "(Kristi) makes this claim of a year-long love affair, which is totally false. If the DNA results are negative, we plan on filing a defamation suit."