It is thought that the tunnel, described as the most ambitious road scheme carried out in the UK in 50 years, could halve journey times between the two cities.
According to the Department for Transport (DfT), all of the routes join the M60 east of Manchester to the M1 north of Sheffield, with four options beginning at the M67.
In addition to the travel benefits the scheme could bring for motorists, experts have suggested it could help to boost the economies of the two cities, the DfT said.
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It could also help to protect the environment by reducing the number of vehicles that have to travel through the Peak District National Park, the DfT added.
Transport Minister John Hayes said: “I want people in the north of England to benefit from quicker, more reliable journeys.
“Today’s study brings us a step closer to building a Trans-Pennine roads tunnel – it would be the most ambitious project since the construction of the first motorways 50 years ago.”
The announcement comes after the publication of a feasibility study last year that said the tunnelled section of the project could measure between 20km and 30km.
If these estimates are realised in the final scheme, the tunnel could be one of the longest of its kind ever built.
A final report is due to be completed by the end of the year that will weigh up the strategic and economic cases for each of the five proposed routes.
No timeframe has yet been set for the building of the project, while a source of funding for the scheme is yet to be confirmed.
It is part of the Government’s next phase of road improvements set to get under way when the current Road Investment Strategy comes to an end at the end of the decade.
The DfT has also published studies looking at improvements that need to be carried out on the A1 in the east of England and the Oxford to Cambridge expressway scheme.