Sanjay Roy, Director in the Department of Health and Family Welfare, filed the affidavit, saying the government has to analyse various factors, such as rail and air links, before deciding on the location.
He said the location of the AIIMS would be decided by the selection committee shortly.
The affidavit was filed on a Public Interest litigation (PIL) from K K Ramesh, who sought a direction to the central government to announce the site for the institute in Tamilnadu.
The State government had suggested five sites - Thoppur, Pudukottai, Sengipatti, Perunthurai and Chengalpattu for setting up the AIIMS.
The court had earlier directed the Centre government to decide on the location before December 2017.
Since it did not arrive at a decision by then, a contempt petition was filed by Ramesh.
On 14 February, the case came up for hearing and the government then sought time, following which the court posted the matter for hearing today.