Cairde na hEirean hopes to stage a procession through the town on July 21.
Last month the group withdrew an application to march on June 2.
The Glasgow-based organisation, which describes itself as the national framework for Irish Republicans in Scotland, has now re-applied to hold an event for up to 400 marchers on Saturday, July 21, at 11 a.m.
The Falkirk Herald understands that the time of the march could be brought forward to 10.15 a.m. after a request from Central Scotland Police.
Marchers would assemble at Nethermains Road before proceeding along Stirling Street into Dunipace and eventually dispersing at Herbertshire Castle Park.
Denny & Dunipace Community Council will not oppose the application, having previously objected to the timing and route of the march planned for June 2.
The final decision on whether the event will go ahead will be made by Falkirk Council’s civic licensing committee at a meeting likely to take place later this month.
Members of the public have until June 23 to submit comments regarding the application.
Cairde na hEireann last marched through Denny in April last year.
Police praised the behaviour of both participants and observers for their good behaviour.