She said Mr Ford has stated that he will "look into" the request.
The chief minister made a pitch for the unit while she came to the Mayapur ISKCON temple in Nadia district, where she was greeted by Alfred Ford, the great grandson of Henry Ford, the founder of the US auto major.
"I have requested Mr Ford (Alfred Ford) to plan a new manufacturing unit here in West Bengal. They have one in Chennai. He said he will look into it," Ms Banerjee said.
Asked whether he would consider her request, Alfred Ford, whose initiated name is Ambarish Dasa, told PTI, "I have told her that I really do not have very much to do with that anymore, but I will put in a word for her."
Ford India Pvt Ltd, a wholly-owned subsidiary of Ford Motor Company, has an integrated manufacturing plant in Maraimalai Nagar near Chennai in Tamil Nadu.
It was the first visit to the Mayapur ISKCON temple by any chief minister of the state.
Mr Ford meanwhile sought help from the chief minister for making the ISKCON Mayapur a world heritage centre.
"We will surely help them in that. I am so happy to coming here," Ms Banerjee said.
She later said in a tweet that ISKCON Mayapur will definitely be a new landmark in the religious tourism destination, not only in the state and the country, but also in the world.