According Mr Kennedy, funding of £9 million for the scheme is being discussed at Stormont as part of cutbacks.
Free travel on buses and trains was introduced here in 2008.
It is understood budget allocations could not be agreed during Departmental spending discussions.
First Minister Peter Robinson has warned unspecified projects faced being suspended or abandoned unless decisions were finalised in the coming days.
Mr Kennedy has vowed to fight to keep concessionary scheme.