The former Miss World and "Bride and Prejudice" star was admitted to Seven Hills Hospital late Monday night and labor has since been induced, the newspaper said.
There has been no confirmation from Abhishek Bachchan, Rai's husband, or hospital officials regarding her condition, however, the Times said.
"There was tighter than usual security on Tuesday and a crowd had assembled outside the hospital to get news of the junior-most Bachchan's arrival," a source told the newspaper.
Notable deaths of 2014 [PHOTOS]
Meg Ryan, Kiernan Shipka to star in 'Fan Girl'