Party insiders are developing the Bright Blue project in a bid to pull in floating voters.
The project will get under way in October with a series of speaker events and a new website. It is being masterminded by Jonty Olliff-Cooper, a former aide to Tory strategy director Steve Hilton.
A number of special advisers to the shadow cabinet are also said to be on board.
'It's definitely not for the traditional rank and file,' said Olliff-Cooper. 'We're primarily aiming at people who are not sure for which party they would vote.'
Some Tory insiders suggested the new website would be a welcome addition to the Tories' internet presence, alongside the influential ConservativeHome blog.
'ConservativeHome is seen as too right wing - it jars against the modern, progressive Conservatism for which David Cameron stands,' one Conservative source told PRWeek. 'There needs to be a place for progressive Tories.'
Olliff-Cooper said a new website would be 'part of the mix but not the most important part'.
He added: 'ConservativeHome doesn't always reflect accurately the genuine opinions of everybody in the party or around the party. But it's really good and we wouldn't want to copy it or usurp it - we're working with it.'
Bright Blue is thought to have the support of the Tory leadership but will operate independently.
'Lots of people who want to be part of it are advisers. We have very strong informal links (to the leadership), but no formal links,' said Olliff-Cooper.