The information came against the backdrop of reports claiming that the militant group had planned to execute the priest Tom Uzhunnallil on Good Friday last week. However, there has been no report of any harm to him so far.
There is no verifiable information with the government on Father Tom Uzhunnallil, the sources said.
Uzhunnalil had gone missing in Yemen after the Islamic State terrorists attacked a care home run by Mother Teresa's Missionaries of Charity.
Four foreign nuns, including an Indian, working as nurses were among those killed.
Last week, External Affairs Minister Sushma Swaraj had said India was making all efforts to secure the priest's release. Sources said the government has even approached the Vatican in this regard.