The local authority said that the move is part of aims to improve air quality and reduce the botough's carbon footprint.
Councillor Carolyn Healy, the council's cabinet member for climate change, green spaces, natural and historic environment and cultural services, confirmed it had submitted a bid for funding to the Government.
It would allow the council to put in 44 electric vehicle charge points across the borough – located in 10 council-owned car parks and accessible 24 hours a day, seven days a week.
Each charge point would feature two sockets, so a total of 88 cars would be able to be charged at the same time.
The council said it expects the Office for Zero Emission Vehicles to review its funding application within the next couple of months and, if successful, installation would be planned to start later this year.
Councillor Healy said: “Individuals and organisations across the borough are really getting on board with the fight against climate change. We hope our funding bid for these charge points is successful as it will offer us another way to help people live even more sustainably in Telford and Wrekin, while also saving drivers money on fuel costs.
“The sooner we can switch over to zero-emission vehicles, and indeed walking or cycling for shorter journeys, the better for our planet and for air quality locally.”