"I can't hardly believe that," Barbara told the Desert Sun. "It's just a bunch of junk. There's always junk written - lies that aren't true."
Ronan himself took to Twitter to respond to the rumours. "Listen," he joked."We're all *possibly* Frank Sinatra's son."
In a new interview with Vanity Fair released earlier this week Mia confirmed that Frank may be the father of her 25-year-old son Ronan, and not her then-partner Woody Allen.
Addressing questions over Ronan's parentage that have been around for years, Mia was asked pointblank if her son with Woody might actually be the son of Frank
"Possibly" she replied, although no DNA tests have been done.
Mia Farrow and her son Ronan
The 68-year-old said that Frank was "the great love of her life", saying, "We never really split up."
When Vanity Fair asked Frank's daughter Nancy Sinatra Jr about Ronan being treated like a member of her family, she replied, "He is a big part of us, and we are blessed to have him in our lives."
Mia and Frank were married in 1966 in Las Vegas when she was 21 and he was 50. Just 18 months later, their marriage fell apart and divorce followed in 1968.