"And suggestions for names are very welcome guys. Something with "A", " the 35-year-old posted on micro-blogging site Twitter.
His wife, Aishwarya Rai, gave birth to their first child Nov 16 at Mumbai's Seven Hills Hospital and since then, the Bachchan family is receiving congratulatory messages from around the globe.
"To receive all this love from all of you. Oh ya! And our crew grows past 800, 000. A huge welcome to all the new ones...And the congratulatory messages still pour in. Thank you so much guys. All of you are wonderful and so sweet. My daughter is so blessed, " he further posted.
While Abhishek is enjoying his fatherhood, megastar Amitabh is in seventh heaven after becoming a grandfather for the third time and says it is difficult for him to stay away from his granddaughter.
"Difficult to tear yourself away from the 'little one', but now home to replay videos and stills and wait for her to come home...Shooting 3D camera stills and movie of the 'little one'... Amazing! Child is the Father of man... Never had this at my birth, " the 69-year-old posted.