Dutt's application, submitted around 20 days ago, is being processed, sources said.
While confirming receipt of an application from the 53-year-old actor for parole, Jail Superintendent Yogesh Desai declined to divulge any details about the ailment for which he intends to seek treatment.
"We have forwarded his parole application to the divisional commissioner, who will take a decision. The divisional commissioner will get a detailed report from the concerned police stations and then decide on the application. While granting parole, the conduct of Sanjay Dutt will also be considered," Desai said.
The actor was convicted by a TADA court for illegally possessing a 9 mm pistol and an AK-56 rifle, a part of the consignment of weapons and explosives brought to India for coordinated serial blasts that killed 257 people and injured over 700 in March 1993.
The Supreme Court had in March this year upheld his conviction under the Arms Act but reduced the six years to five.
He had already served a-year-and-half behind the bars before the apex court's judgement and is undergoing the remaining sentence of 42 months.
Dutt was sent to Arthur Road Jail in Mumbai on May 16 after he surrendered before a designated TADA court and was shifted to Yerawada prison six days later.