It would be operated by the Isle of Man-based regional carrier Citywing and start in October.
Flybe has also applied to run weekday return flights between Derry and Birmingham from 2016.
The routes are among 19 bids from smaller UK airports for funding from the Regional Air Connectivity Fund.
A total of Â£56m will be available to cover three years of support.
Other potential new routes to Northern Ireland would be to the north of England.
Stobart Air wants to run a service between Belfast and Carlisle.
Links Air has bid for a connection to Durham.
The 19 routes have passed an initial application stage and will now be subjected to "strategic and economic appraisal" before final decisions are made by July.
City of Derry airport could have a new, week-round route to Dublin, with the new service shortlisted for help from the government.