He raised the issue during his meeting with Union Health Minister Harsh Vardhan here.
The latter sought a detailed proposal from the state in this regard, a statement by the state government said.
The Chief Minister said he had, in separate letters to the Union Health and Finance Ministers, written to seek the Centre's permission to dedicate the second AIIMS to the Sikh Guru.
Amarinder Singh pointed out that Finance Minister Nirmala Sitharaman had assured consideration of the matter after the release of the Union Budget.
The first AIIMS is already coming up in Bathinda and the state has proposed the second one either in Ludhiana or Jalandhar.
Talking to reporters after his meeting with the Health Minister, Amarinder Singh said all clearances for the AIIMS project in Bathinda had been given by the state government and nothing was pending.
He said Harsh Vardhan had said that he would consider the demand after receiving a formal proposal.
The Chief Minister also sought from the Union Minister approval for a PGI Satellite Centre at Ferozepur.
The state has transferred land to the PGI but the file is pending for approval with the Union Health Ministry.
Ferozepur is a border district and one of the 120 backward aspirational districts selected by Niti Aayog for development, the Chief Minister said.
The problem of drugs also came up for discussion, with the Chief Minister reiterating his demand for a national policy on drugs.
Amarinder Singh said he had sought central assistance for drug treatment, to which the Union Health Minister had said his department would be happy to support the state's efforts.
( With inputs from IANS )