The physicist told BBC Radio 1: “We have some new missions going to Mars called ExoMars which the UK are involved in.
“It is searching for signs of life below the surface of Mars.
“So there is certainly no doubt that there are Martians.”
The ExoMars programme is a groundbreaking project to discover whether there is, or has ever been, life on Mars.
It is a collaboration between the European Space Agency and the Russian Space Agency and is formed of two parts.
Mr Cox added: “There is one theory that we could be Martians because it is possible that life began on Mars over four billion years ago.
“It came to the Earth on meteorites so not in spaceships or anything, but on meteorites that got knocked off Mars.
“There are bits of Mars that land on Earth and the life got delivered to Earth and therefore, we are Martians.
“It is not the most likely theory but it is a possibility that people discuss.”
A rover designed and built in the UK will land on the Red Planet in 2020.
The ExoMars Rover will collect soil samples to look for evidence of life on Mars.
NASA has previously said it aims to get the first humans to Mars somewhere between 2030 and 2040.