The Supreme Court had on August 16 asked the senior politician, who had earlier approached the apex court, to move the Delhi High Court with his plea.
Swamy's plea, in which he has questioned the action taken by the government under the policy, is likely to be listed for hearing on Wednesday.
He said Foreign Investment Promotion Board (FIPB) cleared the proposal but the airline does not exist and FIPB cannot give nod to greenfield projects.
Malaysia's largest budget-carrier AirAsia has set up a joint venture with the Tata Group and Telestra Tradeplace to launch the regional airline in India.
AirAsia India will be based in Chennai in which the Malaysian carrier will hold a 49 per cent stake. Initially, AirAsia plans to invest USD 30 million in the company.
In his PIL, Swamy has challenged the clearance granted to the proposed airline on the ground that according to the policy, foreign investment is only permitted for an existing airline but AirAsia India was not an existing carrier.