Peake, 45, believes humanity is entering a new and "very exciting" era of space exploration in which people like Musk, whose company SpaceX successfully launched the reusable Falcon Heavy rocket earlier this month, could speed the process of putting the first human on Mars.
The astronaut, who completed his mission on the International Space Station in 2016, added that he was looking forward to the Deep Space Gateway, a space station project run by multiple agencies aimed to launch manned missions to Mars, saying it will be the key to the future of human exploration in space.
"[The Deep Space Gateway] paves the way for both lunar landings and, because of the orbit it [will be] in, that paves the way for [a] Mars transportation system," Peake said.
The construction of the Deep Space Gateway is likely to begin in 2022, according to the astronaut.
"Humans on Mars — I think will be late 2030s. That's what the government space agencies and the International Space Exploration Group are working towards," he said, adding that those pioneering commercial space flight such as Musk could bring the date forward. "It could be that some of [these people's] programs bring that date forward. But, late 2030s would be a realistic time frame."
The Tesla billionaire's Falcon Heavy booster is now the most powerful rocket in operation after it was successfully launched and retrieved earlier this month from Cape Canaveral in Florida.
"We have seen the ambitions of people like Elon Musk, there are several other companies that also have ambitions to send people to Mars. I think that we will end up working very closely with these companies in public-private partnerships when we eventually go to Mars." Peake said.
The father of two — dubbed Major Tim, after David Bowie's fictional Major Tom astronaut featured in his iconic song 'Space Oddity' — has previously asserted that he would like to be one of the first to visit the Red Planet.