"The information we have so far is that they are alive because we have no other information to prove that they are not alive," External Affairs Ministry spokesperson Gopal Baglay told reporters.
He said the government was in touch with all the countries "which can help us and are helping us in this matter".
"What steps have been taken in this regard are sensitive. I do not want to say anything more about it," Mr Baglay said, adding that the government "is doing everything possible" in this matter.
The Indians were taken hostage in ISIS-held Mosul in 2014. However, no demand has been made so far for their release.
Mosul is witnessing one of the fiercest fights between ISIS terrorists and joint Iraqi and US forces. The US-backed military offensive to recapture the Iraqi city entered its ninth month on Friday.
ISIS terrorists overran the city in 2014 and imposed brutal Islamist law there. The United Nations refugee agency UNHCR said over 100,000 civilians were trapped there and the ISIS was using kids as human shields.