Goswami is expected to brief Modi about the "priority issues" of the home ministry.
He will be briefing Modi about the steps being taken to check activities of terror outfits and infiltration from across the border and action plan being implemented to deal with the Maoist menace, sources said.
The meeting would be a familiarisation exercise by the Home Ministry for the Prime Minister-elect about country's internal security situation.
They are likely to include matters regarding internal security, formation of a separate state of Telangana and the Delhi assembly polls.
Goswami assumed the office of Secretary of Ministry of Social Justice and Empowerment on 2 July 2012. He remained in this capacity until 27 April 2013, when he was appointed the officer on special duty in the Ministry of Home Affairs. He was named Union Home Secretary by the appointing committee of the cabinet chaired by Manmohan Singh.