The railway authority has put forward two concepts - a visitor centre and viewing platform linked by a lift on the north side and a smaller base for more challenging guided walks to the top of the south tower.
The plan would cost £12 million to £15m to deliver.
A video outlining the proposals suggests a glass-ceiling centre could be tucked under the massive steel structure at North Queensferry, opening up a "cathedral-like" view above.
A lift would take groups to the top of one of the towers more than 300 feet above the Firth Of Forth.
The second concept would allow public access from South Queensferry along an existing walkway under the approach span, close to Dalmeny Station.
Groups of 15 people wearing safety gear would then be able to take guided tours along the bridge to the top.
David Simpson, route managing director at the rail authority, said: "After 10 years spent restoring the bridge to its full glory, and in advance of the application for world heritage listing, these plans will offer the public the chance to visit the bridge and see it close up for the first time.
"We are hugely excited by these proposals and believe they have the potential to be developed into an important new visitor attraction for Scotland. While these plans are still at development stage, we believe the options can be delivered without impacting the well-loved view of the bridge. Any infrastructure on the bridge will be less visible than the existing scaffold platform and all buildings designs will be of premium quality."
"We would love to see these plans at least partially realised by 2015 to coincide with the bridge's 125th anniversary. Any profits would be reinvested into the upkeep of the bridge."
The bridge links Edinburgh with Fife and the north, and carries more than 200 trains a day.
Scottish Transport Minister Keith Brown, speaking on behalf of the Forth Bridge Forum, said: "I welcome Network Rail's exciting and ambitious plans to combine a historic and vital part of Scotland's transport network with a breath-taking attraction for visitors to enjoy."