The Apprentice Boys of Derry wants to hold the procession, which would march past Tynecastle Stadium, for the second time on Saturday, May 26.
The event would take place after the end of the SPL season, but community leaders are still calling for the route to be changed because of the potential for trouble.
Maria Kelly, chairwoman of Gorgie and Dalry community council, said it planned to lodge a formal objection.
She said: “At our last meeting, we were told it was not an appropriate place to be having the march, considering the nature of the band and the fact the marchers could be marching past the football stadium if the route is going to be the same as last year.
“Over the last 18 months we’ve been getting stories of unwelcome behaviour in the area associated with football fans.
“The council has also been told by some members of the community, particularly the Polish community with their Catholic background, that they would be made uncomfortable by the presence of the march. We’re just trying to prevent an awkward situation.
“We are concerned that the march could provoke a response. I am worried it could well be an aggressive response.”
She added: “We recognise they have a right to march. We are not saying that it should be stopped. We’d just prefer it if it did not go through Gorgie and Dalry.”
The city council has confirmed it has received the application and will consider it at a meeting of its licensing committee on April 20.
Michael Borland, vice- president of the Scottish Polish Cultural Association, said allowing the procession to take place would not be a problem when no major fixture was due to take place.
He added: “If the council gives the go-ahead then they should be allowed to march. I do not think the Polish community in the area would have any problem.
“I often visit the area and buy products from the shops there and no-one has said to me that there are tensions between communities.
“I am not aware of any animosity.”
A city council spokeswoman said: “The council has been notified of an intended procession and this will be considered in due course.”
No-one at the Apprentice Boys of Derry – a Protestant fraternal society with clubs throughout the UK and Ireland – was available for comment.