Widespread flooding in the counties has left buildings damaged and led to hundreds of people being evacuated from their homes.
Roads and rail services, including the Dawlish line that links Cornwall with the rest of the country, are still closed.
David Cameron visited both counties to assess the damage earlier this week and vowed to look at alternative mainline rail routes.
Responding to a question from Liberal Democrat MP for Torbay in Parliament earlier this week about whether money will be made available to “market” the south-west to potential visitors and businesses that have lost bookings, the Prime Minister said business leaders had asked him to fund campaigns declaring the area is “open for business”.
He added: “I will take every opportunity I have to help with that issue. When the Dawlish line is restored, it will be a big moment to market the benefits of Devon and Cornwall, where I have been on holiday myself.”
A spokeswoman for the Prime Minister would not offer any further information on the nature, size and when the campaign would launch, whether it would be taxpayer funded or in partnership with tourism bodies.
Vist England is currently running a Twitter campaign using the hashtag “open for business” in the hope of persuading people put off by the floods to visit during half-term next week.