12-year-old Zanai is Bhosle's son Anand's daughter and she has already made her singing debut in 2013 film 'Mai', which starred the legendary crooner.
Bhosle also shared the stage with Zanai at a music award show early this year.
"I have done everything I want in life- singing, acting, TV shows, stage shows. I also recently walked the ramp during a fashion show. I think my next target is to groom my grand-daughter as a playback singer.
Reflecting on the current scenario in the Hindi film music industry, the 81-year-old singer said she sometimes feels annoyed when she hears outrageous lyrics in songs of today like 'Halkat Jawani', 'Munni Badnaam' and 'Lungi' among others.
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"Item songs have become a fashion now. I think there is a scarcity of good lyricists. I find songs very gibberish. But then there are also songs like 'Jab Se Tere Naina' and some by Pakistani singer Rahat Fateh Ali Khan," she said.
"The challenges that I had to face during my early years were humongous. There were many established singers and it was difficult for me to get into the industry. So, I decided to change my style of singing.
"'Eena Meene Deeka' was the first song I sang trying the new style.. Although the old people criticised me a lot, I had found many fans and that is how it started," she said.