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The woman is thought to have discovered she was pregnant only after their relationship ended.
The woman was living with another man at the time of the alleged affair.
"There is a very real possibility that Heath was the father," Haydn Ledger said yesterday.
If it was confirmed that Ledger was the girl's biological father, it could split his multi-million-dollar estate between his two-year-old daughter Matilda Rose with Hollywood actor Michelle Williams, and his secret love child.
Ledger, who died alone in his New York apartment in January from an accidental overdose of prescription drugs, drew up his will before the birth of Matilda, on whom he doted.
The April 2003 will lists only $145,000 in assets and names the late actor's father, Kim, mother Sally Bell, sister Kate Ledger and half sisters Olivia Ledger and Ashleigh Bell as the beneficiaries.
New York documents also acknowledge Matilda Rose, as Ledger's only known child, as an interested party.
Ledger was still at school at Guildford Grammar when he began the affair with the woman, then aged 25.
Another family source said yesterday: "She had the baby. Everyone lived under the assumption that (the baby) was the daughter of the mother's boyfriend, and that is how she has been brought up."
The woman is now married with a young family.
"I have my children to think about. I really can't comment," the woman said.
Ledger's death has exposed the bitter rift in the family between father Kim and his estranged brothers, Haydn, Mike and Wayne.
The family feud began when Kim became executor of their grandfather Sir Frank Ledger's estate more than 20 years ago.
He borrowed against the $2 million estate, leaving it heavily in debt before he was removed as executor by the WA Supreme Court in 1994.
Heath Ledger nominated accountant Mark Dyson and Perth company director Rob Collins as executors of his will...Celebs and Bubs
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