Designed by Mark Brunel and overseen by his son Isambard, the Thames Tunnel was the world's first underwater tunnel.
The ELL will close in December for 30 months to allow for its extension and conversion to heavy rail, and the museum will install a shelf at low level in a disused brick shaft.
Situated above where the trains run, this shelf will constitute the floor surface of a room allowing vistors to see the tunnel first-hand.
"When people visit the museum, they want to go into the tunnel," said Museum director Robert Hulse."Once they're inside the shaft, they're inside the tunnel, the heart of the project.
It's like visiting the SS Great Britain, you want to go on board the ship, and not to the draughtsman's office at the side."
The increase in space will also allow the museum to display some examples of modern day cutting-edge engineering.
"If Brunel is significant, it's because he's redefined engineering," added Hulse.
"It [the museum] is not just about Brunel, it will be about innovative engineering."
Transport for London (TfL) carried out a feasibilty study into utilising the shaft earlier this year. It has now agreed to undertake a detailed design study, the estimated cost of which is between £30,000 and £50,000.
The museoum will need to raise funds to fit out the space.