The actor is currently best known for his work in the US film industry, including a role in the upcoming Mission Impossible - Ghost Protocol.
A source told The Times of India: "People feel Anil is so involved in his own career, especially now that he's working in Hollywood, that he doesn't know what's happening in Sonam's career. But that's far from the truth.
"Anil remains as involved in his daughter's work as he was right from Saawariya, and advises her on everything.
"He is proud of her. When he receives compliments from the film fraternity for his beti [woman], he first tells her and repeats it to ten other people."
The veteran star recently insisted that his roots remain in Bollywood.
He said: "I am a very emotional person. I just continue being myself, a mainstream commercial hero from Indian cinema. To be honest, Hollywood too has its downside."
Anil will next be seen in the financial thriller Cities with British star Clive Owen.
In May, Sonam compared her father to a "rock star" and praised his energy.
Watch the trailer for Mission Impossible - Ghost Protocol below: