Broad corridors for the tunnel had previously been identified and ministers have today gone further, specifying five routes they wish to consider in more detail.
All five options connected the M1 to the M60 around Manchester.
The most northern option sees the route connect to where the A635 currently passes under the M1 north of Barnsley. The most southern option would link to the M1 just north of Sheffield.
Supporters of the idea argue it could cut transpennine journey times by 30 minutes and remove traffic from the Peak District.
But critics claim it would just add to existing traffic problems at both ends of the tunnel and more efforts should go into encouraging people out of their cars.
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.
“We are already spending £15 billion on the biggest upgrade to the road network for generations.
“This next phase is aimed at creating more vital links, creating jobs and opportunities and helping hardworking families across the country feel the benefits of our investment.”
Sheffield City Council leader Julie Dore said: “Better connecting Sheffield and Manchester will help make a step change for our city regions, the north and the UK as a whole.
“We have been advocating for this project for a long time, alongside other crucial connectivity improvements such as 30 minute city centre to city centre rail travel.
“This is another step forward towards delivering these ambitions and we will continue working as part of Transport for the North to make sure they become a reality.”