In an interview to Vanity Fair, Farrow said that her 25-year-old son Ronan was "possibly" fathered by ex-husband Sinatra and not Allen.
"I can't hardly believe that. It's just a bunch of junk. There's always junk written - lies that aren't true," Barbara told The Desert Sun.
She called Farrow's revelation "a phony deal", adding later singer left nothing to Ronan in his will.
Farrow, who called the singer the great love of her life, was married to Sinatra for 18 months. Sinatra divorced her after she opted to act in 'Rosemary's Baby' over her husband's film but Farrow said they never really split up.
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No DNA tests have been done, but Ronan was treated like a member of the Sinatra family, according to Nancy Sinatra Jr, the magazine said.
Allen broke up with Farrow in 1992 after she found out that he was having an affair with her adopted daughter Soon-Yi.
The actress subsequently took Allen to court alleging the director of molesting their seven-year-old adopted daughter. Allen was disowned by Ronan and his two other adopted children with Farrow. He later went on to marry Soon-Yi.
Ronan, a human rights activist, also weighted in on his mother's comments on his Twitter page: "Listen, we're all 'possibly' Frank Sinatra's son.