Coulson, a former editor at the News of the World, left his job with Cameron in January 2011 after he was implicated in the phone-hacking scandal. He was formally charged last July with criminal violations.
In an article for GQ magazine, Coulson speaks about politics publicly for the first time since he was charged, The Guardian reported Tuesday. He says he thinks the Conservatives and Cameron can overcome their current low standing with voters before the 2015 general election.
But he said the party needs to deal with one problem within its own ranks -- London Mayor Boris Johnson. Coulson said Cameron is well aware Johnson "desperately wants to be prime minister."
"Stabbing David, or anyone else for that matter, in the back would be distinctly off brand -- just not very Boris," Coulson said. "He would much prefer to see David fail miserably in the election and ride in on his bike to save party and country."
Coulson recommended the party needs a "simple" strategy: "Support his good ideas, advise privately on the bad ones, but only engage publicly if absolutely necessary -- and celebrate Boris's considerable successes."
Conservatives must also get Labor leader Ed Miliband "to take a view on the tricky issues opposition politicians love to duck," Coulson said.