The other marine Massimiliano Latorre is already in Italy on health grounds and his stay there has recently been extended by the apex court till September 30 this year.
A vacation bench comprising Justices P C Pant and D Y Chandrachud would hear the fresh plea of Girone on Thursday in which he has sought modification of a Kerala High Court order granting him bail in the case.
Italy and India have been making contrary claims over the right to prosecute the two Italian marines in the case.
Centre had earlier informed the court that international arbitration proceedings in the matter would be completed by December 2018.
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The court had earlier stayed all criminal proceedings, including the trial of the two marines.
While allowing the joint request of India and Italy, the apex court had said the proceedings would remain stalled till the jurisdictional issue about which country has the right to conduct trial was decided through international arbitration.
The complaint against the Italian marines was lodged by Freddy, the owner of the fishing boat 'St Antony', in which the two Indian fishermen were killed when the marines opened fire on them allegedly under the misconception that they were pirates.