It is thought that the actor, who played the role of Masood's brother Inzamam in the BBC soap on and off from 2008 until 2010, went missing after leaving the Royal Court Theatre last week.
The Evening Standard quotes Bhattacharjee's son as saying: "Dad, wherever you are please, please get in contact. We want to know that you are okay and if anyone has seen or heard from him in the last few days please get in contact.
"Please, we are just worried sick. It's completely out of character. He was doing well in his career and everything seemed to be going okay. I just don't know what has happened."
Stephen Fry took to Twitter to rally support to find the actor, retweeting a post from actress Natalie Dew, which read: "Please read and RT. A wonderful actor and lovely man has gone missing.
The actor has also had roles in James Bond and The Best Exotic Marigold Hotel.
Anyone with information on Paul's whereabouts is urged to call the police non-emergency line on 101 or Missing People on 116 000. Get the Inside Soap magazine on your iPhone or iPad