I personally don't think Iran would give the port to Indian navy, bcuz it has shown interest in joining CPEC, which would allow it to sell oil/gas to China, will give it an overland route to China via Pakistan.
However Ajit Doval (India's NSA) had met President Rouhani, asking Indian navy be allowed to use the port, but Iranian reaction (most probably denying this access to Indian navy) is not made public as of yet.
Secret trips to West Asia
One thing to be mentioned here, is Ajit Doval is the same person who went on a secret trip to Iraq two times to negotiate the release of Indian prisoners by Islamic State, intriguingly soon after his visit, IS started making inroads into Afghanistan, to counter Taliban and threaten all neighbors of Afghanistan. Doval has publicly called out to support Baloch separatists & Taliban insurgency to engage to Pakistan, has openly claimed to live undercover in Pakistan for 7 years (obviously an exaggerated claim) , has claimed in a speech that in case of a nuclear war with Pak, some indians might survive to carry on their civilization while Pakistan can be wiped off.
Such a lunatic who is sitting at such a sensitive post in Indian regime, is by all means a security threat to this entire region.