Khan and his wife Kiran Rao announced the birth of their son Azad Rao Khan on December 1 through a surrogate mother.
Speaking at a media event, the 46-year-old actor told the Press Trust of India that he loves spending time and playing with his newborn son.
"It's a great joy being a father again," Khan said. "Both Kiran and I are so overjoyed with our baby being born and I just can't get enough of Azad.
"I tickle his little toe and then I snuggle up to him. Right now he doesn't even know who I am. He's too young but he knows that somebody comes and troubles him everyday. Every two [or] three hours somebody comes and troubles him."
"So, when he gets a little older, he will get to know that I am the guy," said Khan, who already has two children from his first wife Reena - son Junaid and a daughter named Ira.
The 3 Idiots star and his wife - who were speaking to press at the launch of the CDs and DVDs of Rao's directorial project Dhobi Ghat - explained they were keen to hurry home to their son.
"For the first time, Kiran has left the house since the baby was born. So we are also keen to get back fast. It's a miracle. A baby being born is a miracle and nothing comes close to it," said Khan.
The actor also said he would like to pen an autobiography, adding: "When I think about my life, career, relations, the film industry and the experiences, I feel I should write an autobiography. I want to share the experiences and all ... but it is a difficult task."
Khan is currently busy with his co-production Talaash, which also stars Kareena Kapoor and Rani Mukerji.