Khan said Rajan was positive when he met him recently to push the proposal.
"The financial reforms commission headed by Rajan had even advocated Islamic banking. I am sure his appointment as RBI governor would be a big push for the proposal," the Minority Affairs minister told PTI.
He hinted that various stake-holders like finance ministry and RBI are apprehensive of the idea of Islamic banking because of its religious overtones.
"They believe they will be blamed that they are doing it for religious-based reasons. You can have regulator for chit funds companies, tree companies, this company, that company, companies collecting big money and vanishing but you do not want a sharia-compliance institution," Khan said.
The minister said all over the world, Islamic banking system is in practice and it would enable Muslims to save their money for their and country's development.
"They are not saving in bank because earning interest is against the fundamental of their religion," he said, adding that the present banking system based on interest excludes a large number of Muslims.
"We can save so much we can take care of our developmental, educational needs," he said.
In a letter to RBI governor in December, 12, Khan had said the Constitution allowed citizens to practice their faith and it was the state's duty to facilitate people to practice their religions, arguing in favour of Islamic baking.
Khan's predecessor Salman Khurshid, now the Exteranl Affairs minister, had first floated the idea and asked RBI to explore the possibility of establishing Islamic banking in India.