The 68-year-old actress was married to the singer for two years back in the 60s, but it was always thought that Woody Allen was the father of Ronan, who was born in 1987.
Mia was with director, Woody for 12 years between 1980 and 1992.
Mia Farrow with son Ronan
Asked if Ronan - who was born Satchel O'Sullivan Farrow and bares a striking resemblance to Sinatra - was the son of the crooner, Mia told Vanity Fair: "Possibly".
"We never really split up," she added.
Ronan bares a striking resemblance to Old Blue Eyes
Sinatra died aged 82 in 1998, 11 years after the birth of Ronan.
He had three children Nancy, Frank Jr., and Tina, all with his first wife, Nancy Sinatra, who he was married to from 1939 to 1951.
As well as Nancy and Mia, he was also married to Ava Gardner and Barbara Marx.
Barbara has since told The Desert Sun that she doesn't believe Mia's paternity claims, telling The Sun: "It sounds like a phony to me.
"It's just a bunch of junk. There’s always junk written — lies that aren't true," she added.
Ronan also passed comment on the revelations, tweeting on Wednesday: "Listen, we're all *possibly* Frank Sinatra's son."
Woody Allen's spokesperson has since told The Hollywood Reporter that the 'article is so fictitious and extravagantly absurd'.