Union home secretary RK Singh said family members of Kasab, who live in Pakistan, had also been informed by Indian High Commission in Islamabad.
"His family members were communicated through courier by our High Commission. We have the receipt of the courier sent and that was later given to the Maharashtra government," Singh said.
Shinde said so far no one has claimed the body of 25-year-old Kasab and if Pakistan claims it, India would give it to the neighbouring country.
The home minister said there should not be any problem if Kasab is buried in India.
"I do not think there will be any trouble (if Kasab is buried in India) because India has suffered too much and everyone.... and this country has seen the tragedy. 166 people were killed during three days of the carnage" that began on November 26, 2008, he said.
Kasab was hanged in Pune's Yerawada jail at 7.30am, Maharashtra home minister RR Patil said in Mumbai.