"I spoke to a jittery Dawood three times in June 1994...He seemed to be toying with the idea of surrendering but had one worry - his rival gangs could finish him off if he returned to India. I told him his safety would be the responsibility of the CBI," Kumar said in an exclusive interview to HT.
He also told the daily that the seniors who had given Kumar a green signal to talk to the underworld don, later asked him to put an end to the phone calls.
Neeraj Kumar, who is said to be working on a book, was leading the CBI probe into the 13 blasts that rocked Mumbai on March 12, 1993.
Kumar retired as the Delhi Police commissioner in July 2013.
Earlier, the senior Supreme Court lawyer Ram Jethmalani had also said that Dawood had called him up and said that he was ready to surrender but the government didn't agree to his conditions.
Jethmalani said Dawood had kept a condition for the same and said that he wanted assurance that the Mumbai Police would not torture him and would keep him under house arrest.
Meanwhile, former CBI director Vijay Rama Rao said, "No such offer of surrender came from Dawood Ibrahim and even if it came, it was not brought to my knowledge."
He also said that Kumar is doing so to gather readers for his book which is yet to be published.
The 1993 Mumbai bombings were a series of 13 bomb explosions that took place in Mumbai on March 12, 1993 leaving 257 people dead and more than 1000 injured.