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.
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.