The local authority's bid forms part of its continuing Transforming Cities and Connecting Leicester work.
Cities and regions across the UK are bidding for a share of £1.2bn of Department for Transport funding.
Submitted schemes include high-quality walking and cycling links to the south and east of city centre, to better connect the city centre with neighbourhoods and both universities. In the north of the city centre, better links are planned between the city centre and neighbouring regeneration areas at Pioneer Park as well as nearby communities.
A public bike share scheme is also being proposed, along with electric bus proposals on the Birstall Park and Ride route.
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City Mayor Peter Soulsby said: "In submitting this bid to the DfT, we have put forward a number of schemes to build on the work of Connecting Leicester and continue to improve transport links across the city.
"A share of the DfT funding would enable us to bring forward some very significant schemes focusing on better transport infrastructure to support the city's economy, using smart transport technology and encouraging more people to use buses, walking and cycling networks connecting more areas of the city.
"The prospect of a bike share scheme is a very interesting one, and we are currently looking into the details of such a scheme, as well as the logistics of how a scheme could best work for the city."
Leicester Deputy City Mayor with responsibility for the environment, Cllr Adam Clarke, added: "The proposals set out in this bid are key to making sustainable transport in the city more accessible and more appealing to people.
"Developing easy to use smart ticketing, creating a network of comprehensive walking and cycle routes, and introducing electric buses on one of the city's main Park and Ride routes are all big steps towards improving air quality, cutting congestion and making sustainable travel in the city more attractive."
The city council is expecting to hear if it has been successful in February 2019.
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