"My mother Meena Patel wrote a letter to Governor a few weeks ago, requesting to release my father as he is turning blind now," Bajrangi's son Tarun told PTI.
"We have not received any reply so far," he said.
Officials of the Supreme Court-appointed Special Investigation Team and the Governor's office said they had no information about the letter. Naroda Patiya was one of the nine cases probed by the SIT.
He is one of the 31 convicts in the Naroda Patiya case. As many as 97 people of Muslim community were killed in Naroda Patiya area during the post-Godhra riots.
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He was awarded 'imprisonment till death' by the special trial court in August 2012.
The court also awarded 28 years' imprisonment to former Gujarat minister Maya Kodnani in the case, describing the 2002 riots "a black chapter in the history of democratic India".
Bajrangi's appeal against the conviction is pending before the Gujarat High Court.