The 30-year-old covered walkway between the SEC and Finnieston could be redeveloped with £5m from the Glasgow City Region City Deal.
An initial grant of £660,000 has been provided by Glasgow City Council for feasibility, design and procurement.
The bridge is a key connection between the SEC, Finnieston, Pacific Quay and the Exhibition Centre rail station.
The council said that while the bridge was structurally sound, the canopy was nearing the end of its life cycle.
The whole area is to benefit from £114m in City Deal funding to help connect "economic drivers" in the area including the University of Glasgow, the SEC, the Queen Elizabeth University Hospital, and the digital media quarter at Pacific Quay.
Council leader Frank McAveety said: "The redevelopment of this bridge highlights our commitment to further develop the West End and Waterfront.
"The sky is the limit for these areas and I am delighted that the Glasgow City Region City Deal is contributing to them achieving their full potential."
The bridge is currently under a long-term lease to the SEC.
SEC chief executive Peter Duthie said: "First impressions are very important and with a new brand, a world class arena and countless incredible events coming on site it is important that our campus facilities are up to scratch.
"In many cases the covered walkway or 'Smartie tube' is the first thing visitors experience when coming to the Scottish Event Campus and so we are delighted with the news that it is to be upgraded."
The UK and Scottish governments are to give Glasgow and the seven neighbouring authorities £500m for the City Deal, and the councils are to borrow a further £130m for capital investment.