Azmi was killed in 2010 in Mumbai.
Mehta might request the state government to rename a road at the Kurla Taximen's Colony, where Azmi worked from and was eventually murdered.
"I really want this to happen. It will be a fitting tribute to a hero of Mumbai," Mehta said in a statement.
"'Shahid' is an underdog story of a man's fight against injustice and there are many Shahid's not just in Mumbai but across India who stand up for justice every single day. An inspirational story like Shahid's needs to be remembered," he added.
"Shahid", starring Rajkumar Yadav, has been co-produced by UTV Spotboy, Sunil Bohra and Anurag Kashyap.