I learned the hard way, that it is indeed not possible to transfer funds from savings account in India (State Bank of India) to my NRI account (NRE account in State bank of Travancore).
When I initiated the transfer, the fund got debited from my account. The next day, the fund was returned to my savings account and the status of the transaction was mentioned as “Failure – Credit to NRE Account”.
Called up the customer care at SBT, who said it is indeed not possible to transfer funds to my NRE account, and I may credit funds only via currency exchanges here in UAE.
It is now confirmed! Do not attempt to send funds from savings account in India to another NRE account!