The role he offered her was taken on by relative newcomer Ileana D'Cruz after Kaif dropped out.
Basu told the Hindustan Times: "I wanted to cast them Ranbir Kapoor and Katrina. They look nice together. I was glad when Katrina said 'yes' as she was my first choice for the role. I had approached her for the character that Ileana finally ended up doing.
"Things didn't fall into place with Katrina because Rockstar got delayed, which ultimately was affecting Barfi!'s schedule. Therefore, we had to reschedule everybody's dates, which took time. Things clicked with Ileana and I'm glad she came on board."
The paper claims that Kaif was not keen on sharing the film with another female lead.
Barfi! sees Kapoor and Priyanka Chopra play a couple with disabilities whose relationship is disrupted by the arrival of the former's first love, played by D'Cruz.
D'Cruz has described making her Bollywood debut in the film as "amazing".
A set insider revealed in March that Kapoor and D'Cruz have "great chemistry" even in scenes without dialogue.
Watch a trailer for Barfi! below: