The film starred Ranbir Kapoor as a deaf and mute man who falls in love with an able-bodied woman.
He told The Times of India: "We are discussing some possibilities. But it's too early to talk about them.
"A sequel is definitely out. Where will I take Barfi's story when he is already dead? If the producers feel comfortable with the idea they're welcome to do a sequel to Barfi! The Bhatts did a sequel to my film Murder. I was not involved with it."
The comedy drama has been put forward as India's entry for the 'Best Foreign Film' category at next year's Oscars.
Basu added: "The Oscar nomination is like a bonus. On the day it was announced I was locked away writing my next script, so I had no clue until late in the night.
"Let me not be overly modest and admit I knew Barfi! would be liked by critics and would go to various film festivals. It has already been selected for the Pusan, Marrakesh and the Taipei film festival.
"What took me by surprise was the popular mandate given to Barfi! I never expected it to be so popular.
"I always looked up to Raj Kumar Hirani for making inspirational films that were warmly embraced by the masses. Now Barfi! seems to have done the same."
In September, the director said that the film deserves to have been selected for the Hollywood awards ceremony.
He has previously criticised the Indian film industry for accusing original filmmakers of plagiarism.
Watch Ranbir Kapoor in the trailer for Barfi!: