"I believe that our riflemen deserve to be back home for Christmas and we will do everything we can to bring this about," Staffan De Mistura told Italy's Radio Anch'io.
Salvatore Girone and Massimiliano Latorre are due to stand trial over the killing of two fishermen in Kerala in February 2012 while the Marines were guarding an oil tanker.
"I am an optimist by nature, but we have had some unpleasant surprises along the way and I am therefore cautious," said De Mistura, who is currently in New Delhi to hold meetings with the Marines, their lawyer and Indian officials.
India in March refused to allow Italy's ambassador to India to leave the country amid a diplomatic row that erupted between the two countries when Rome broke a promise to return Girone and Latorre to India for trial.
The Marines had been allowed to go home to vote in the national elections.
The row was defused when Italy sent them back after receiving assurances they would not face the death penalty.
Girone and Latorre claim they mistook the unarmed Indian fishermen for pirates and Italy claims the incident took place in international waters, meaning India should not have jurisdiction over the case.
No trial date has so far been set for the pair. De Mistura, however, said it was possible the trial could begin in September and was likely to be brief.
"I have the impression that there is just as much interest on the Indian side to see this issue resolved rapidly and justly," he said.
The Marines are living at the Italian embassy in New Delhi while they await trial.
--IANS (Posted on 17-08-2013)