Rao, who is here for two-day talks with her Pakistani counterpart Salman Bashir, said the External Affairs Ministry was in touch with the government of Rajasthan, which is seized of the matter.
She said she was hopeful that the case would be resolved.
Ashok Gehlot, Chief Minister of Rajasthan, had cleared the mercy plea of Chishty, following which it was forwarded to the Governor.
Prime Minister Manmohan Singh on Monday asked Home Minister P Chidambaram to examine if the request of a Supreme Court judge for pardon to Chishty could be considered on "humanitarian" grounds.
Singh had forwarded to Chidambaram the letter of request received from Justice Markandeya Katju.
A sessions court in Ajmer had awarded Chishty life sentence on January 31 this year in a murder case after an 18-year-long trial. He had also filed an appeal in the High Court but his bail plea was rejected.
Chishty had got involved in a fracas during his visit to Ajmer in 1992 to meet his ailing mother and in the melee one person was killed leading to his arrest.
During the trial period, the sessions court, which had granted him bail after few days of the incident, had ordered Chishty not to leave Ajmer and he was re-arrested after his conviction. During the bail period, he spent time at his brother`s farm in Ajmer.