A bench of justices K K Sasidharan and G R Swaminathan gave the direction during the hearing of PILs on the matter.
Earlier, the Centre's advocate said a committee formed to inspect and decide the site would file its final report shortly.
Initially, when the matter came up this morning, the judges asked the government counsel to get information as to when the announcement regarding the site would be made and adjourned the hearing till noon.
Petitioner K K Ramesh had sought a direction to the Centre to announce the district where the institute would be set up.
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Another PIL litigant R K Baskar wanted the AIIMS to be set up in Madurai itself.
In the previous hearings, the counsel for the centre had said it was for the union government to finalise the location.
When the judges referred to the counter affidavit which said it was for the state government to decide, the central government pleader had sought time.