The SpaceX CEO says he has finally worked out how to do it, and told the BBC he would reveal further details later this year or early in 2013.
Musk is one of Nasa's new commercial partners, building systems to take cargo and crew to the space station.
He has developed his own rocket and a capsule for the purpose.
The Falcon 9 launcher and the Dragon vessel are expected to give the first full demonstration of their capabilities next month on an unmanned sortie to the orbiting outpost.
Elon Musk describes his Mars vision in Scott's Legacy, a BBC Radio 4 programme presented by Kevin Fong. The programme examines the future of exploration.
It can be heard on iPlayer but you can also listen to Kevin's extended interview with the SpaceX chief on this page.
In the discussion, the California entrepreneur says key technology breakthroughs are dramatically lowering the cost of space access to the point where a mission to the Red Planet will very soon become a realistic financial prospect.
"My vision is for a fully reusable rocket transport system between Earth and Mars that is able to re-fuel on Mars - this is very important - so you don't have to carry the return fuel when you go there," he said.
"The whole system [must be] reusable - nothing is thrown away. That's very important because then you're just down to the cost of the propellant.
"We will probably unveil the overall strategy later this year in a little more detail, but I'm quite confident that it could work and that ultimately we could offer a round trip to Mars that the average person could afford - let's say the average person after they've made some savings."
The entrepreneur described this as about half a million dollars. He conceded the figure was unlikely to be the opening price - rather, the cost of a ticket on a mature system that had been operating for about a decade. Nonetheless, Musk thought such an offering could be introduced in 10 years at best, and 15 at worst.
"Land on Mars, a round-trip ticket - half a million dollars. It can be done," he asserts.
Leaving aside how one might define the wealth of an "average person", this is quite a claim.
To put it in some context - Nasa itself is commissioning its own rocket and capsule system from more established aerospace companies that the agency expects eventually to use on Mars missions.
Few elements of this multi-billion-dollar system will be re-useable and its maiden manned flight - probably a loop around the Moon - may not occur until the early 2020s. A Nasa-led manned mission to the Red Planet is unlikely to happen until the 2030s, and that could be optimistic.