The proposed tourist development would also include a visitors' centre and hotel, with a restaurant overlooking the water.
The Humber Bridge Board said it hoped to submit a planning application by the end of the month.
If approved the new centre could be open at the end of 2017.
The proposal would see visitors travelling under the bridge in a glass gondola before changing to a glass lift to ride to a platform on the top of the North tower.
Construction began in July 1972, taking eight years to complete
It is held up by 44,117 miles (71,000km) of steel wire, almost enough to travel twice around the world
The bridge is 7,283 ft (2,220 m) long from shore to shore
It weighs more than 500,000 tonnes
With a central span of 4,626 ft (1,410m), it is the seventh longest suspension bridge in the world
It was officially opened by HM the Queen on 17 July 1981
Source: Humber Bridge Board
Bridge Master Peter Hill said the scheme was about "making the best of what we've got".
"People have for years had wanted to get more access to their bridge, so we're going to make it happen, " he said.
Mr Hill said the project would be financed by the bridge board but "would not be funded from bridge tolls".
A public exhibition of the proposals has gone on display at the bridge.

Broken swords and spearheads were found by archaeologists on the RSPB Scotland nature reserve.
Twelve pieces excavated from several different weapons have been handed over to Kilmartin Museum in Argyll.
RSPB Scotland reserves archaeologist Jill Harden said they had probably been deliberately broken and thrown into a loch as part of a religious ceremony.
"This is the first discovery of this size from Argyll for many years," she said.
"The items were recovered from what had once been a freshwater loch - it seems that they had been purposely broken and cast into the waters as part of a ceremony, most likely as offerings or gifts to the gods or goddesses of the time.
"It is recorded that bronze swords were found on Coll in the 19th Century during drainage works, but their whereabouts today are unknown."
The archaeological investigation was directed by the Treasure Trove Unit, National Museums Scotland and RSPB Scotland.
Trevor Cowie, from National Museums Scotland's department of Scottish history and archaeology, said: "While a fair number of objects from this period have been discovered in the west of Scotland in the past, we generally know very little about the precise places where they were found.
"Archaeological techniques have developed dramatically since those 19th Century discoveries were made, so we have a great opportunity here to resolve many unanswered questions about life on Coll some 3,000 years ago."
The weapons can be viewed at the the Isle of Coll's An Cridhe community centre on Thursday and Friday.

Uefa's executive will not allow their congress to discuss Jersey's bid as the island is not recognised by the United Nations as an independent nation.
Representatives from Uefa visited the island, which is a crown dependency of Great Britain, in September to meet with Jersey football officials.
"This was the response we expected," said Jersey FA president Phil Austin.
"From a footballing perspective we more than meet the criteria.
"In rejecting our application, the executive of Uefa have said that they're not putting our application forward to the congress. We don't think the executive have the authority to do that, we think it should go to congress," Austin told BBC Sport.
Jersey submitted a bid to leave the English FA and join Uefa in December 2015, following the acceptance of Gibraltar and Kosovo, who are not independent nations.
But Gibraltar's initial application in 2007 came before the rules were changed, while Kosovo, who joined Uefa in May and played in their first World Cup qualifier in September declared independence from Serbia in 2008.
"I have no idea how long it's going to take, we are waiting for a court date hopefully within the next six months, but I don't know," added Austin.
"We are watching the costs very carefully and we will take it each step at a time and managed our budget accordingly.
"One or two people have stepped forward who believe in what we're doing and will help us with our funding."
Plans have been unveiled for a glass lift to take tourists to the top of one of Humber Bridge's 510 ft (155m) high towers.
[NEXT_CONCEPT]
Bronze weapons believed to date back about 3,000 years have been discovered on the Isle of Coll.
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Jersey are to appeal to the Court of Arbitration for Sport (CAS) after their bid to join Uefa was turned down.