The officials say in the case of Iran, the lifting of sanctions has paved the way for direct relations.
Three Iranian banks, Bank Pasargad, Saman Bank and Parsian Bank, are in queue, according to information made available to the Rajya Sabha.
Two banks from Pakistan, MCB Bank and United Bank, have sent proposals to the Reserve Bank of India (RBI) for opening branches in the country.
Bank of Montreal (Canada), ING Bank (the Netherlands), and Busan Bank (South Korea) have also sought permission from RBI to set up branches here.
Recently, the Islamic Development Bank (IDB) said it would initiate talks with RBI to allow it to introduce Islamic financing, raising of capital in accordance with Sharia law.
This comes at a time when foreign banks in India have been reducing their footprint because of trouble in their home markets and rising competition from Indian banks.
Rising bad loans have forced some foreign lenders to slow down. Standard Chartered Bank, the largest foreign bank in India in terms of branches, has decided to reduce its unsecured retail and corporate business in the country.