Parts of Madeira Terraces, have been fenced off since summer after warnings the Victorian structure could collapse.
Council leader Warren Morgan revealed in a Facebook post the authority has applied for Â£50,000 from the government's coastal revival fund.
Homeless people had been sleeping under the arches.
Mr Morgan said: "It is the preliminary step of the restoration process and whilst it does not detail our plans, I hope that it shows that a process, however slow, is underway."
The concern with the structure surrounds the corrosion of steel beams embedded in concrete which supports the deck of the terraces.
It was announced in October that more fencing was to be installed after rough sleepers were discovered.
At the time, Mr Morgan said the site would be secured and staff would help people find safer accommodation.
Brighton's crumbling seafront arches may be restored after the council revealed it has applied for funding to help redevelop the site.