The cash would be used to install charging points for electric cars.
Dundee could be in line for a £36 million grant towards low- emission vehicles.
The cash would pay for the infrastructure for electric cars, including charging points.
If successful, the council will also distribute funds to other Scottish cities.
Chris Elder, taxi branch secretary of the Unite union, said he had been made aware of a feasibility study that had been carried out by the city council prior to applying for the grant.
“They have now applied for the grant,” he said.
“As far as I am aware the council will hear in around six to eight weeks from now if they have been successful.”
Dundee is competing with 12 other cities hoping to be named as one of the country’s first Go Ultra Low Cities.
The city council will find out if it has been selected when the winners are announced later this year.
Poppy Welch, head of Go Ultra Low, said she was “excited” by the passion and innovation on display from each competing city.
