There are mainly two things that connect India with ASEAN, one is Buddhism and the other is Ramayana, Ms Swaraj said.
"From the Government of India's side, we would like to institutionalise the relationship through a permanent mechanism so that the youth of ASEAN countries can partake our cultural and religious ethos and become true ambassadors of India in their countries," the External Affairs Minister said on Monday.
The minister also said that India cannot become a member of ASEAN because of geographical reason as this grouping is of South East Asian nations while India lies in the South Asia.
Ms Swaraj was addressing the India-ASEAN Youth Awards function in New Delhi on Monday.
She also highlighted the strong cultural ties that bind India and the ASEAN countries.
Ms Swaraj said the cultural bonds between India and ASEAN countries were centuries old and the "onus was on us to propagate this special relationship amongst the youth in both the regions".
ASEAN (Association of Southeast Asian Nations) is a multilateral body whose member countries include Thailand, Indonesia, Singapore, Brunei, Laos, Myanmar, Cambodia, Malaysia, the Philippines and Vietnam.