Banerjee made the request during Singh's three-hour visit to the city during the day.
She later told reporters that the prime minister had asked her to give a detailed note in the matter so that the Centre can look into it.
Banerjee had yesterday paid a visit to Kapil Muni temple in Sagar Island in South 24 Parganas district of the state , the venue of the annual Ganga Sagar mela which draws lakhs of devotees from across the country every year.
The temple, about 140 km from Kolkata, is one of the most popular pilgrim spots in the country.