Advani made the announcement after holding talks with visiting British Home Secretary David Blunkett. Bleach is serving a life sentence in Calcutta for air dropping arms for a militant group seven years ago.
"There is an outstanding matter pending between India and Britain," Advani said. "There has been a longstanding demand that Peter Bleach be released."
The matter, he added, "has been actively discussed" and the law ministry had given the clearance. "It should be possible to release him soon," Advani said.
Asked when the release would take place, he said, "it will be
formalised very quickly."
Blunkett responded by thanking Advani, who is also the home minister, saying he was "tremendously pleased."
"I have a reputation for sending and keeping people in prison," Blunkett said. "I am very pleased that the minister is prepared to let one out."
Bleach and five Latvian pilots were charged with waging a war against India after they dropped crates of assault rifles and anti-tank missiles to militants in Purulia in West Bengal on December 17, 1995.
"I am in jail because I am a British national"
British gun runner
A city court sentenced Bleach and the Russians to life imprisonment in February, 2000.
The Latvian pilots were released from jail in July of that year after India's president remitted their sentences.
Bleach, 51, appealed to the Calcutta High Court in September 2002 saying he was being discriminated against as he was being held in jail despite his repeated appeals to the Indian government.
In his petition, Bleach said the five Latvians who had piloted the aircraft carrying the arms and ammunition were released from jail on the grounds of their Russian citizenship.
"I am in jail because I am a British national," he said. Bleach also resorted to a hunger strike to press his demand for the same treatment the other pilots had enjoyed.