Those facing the ax were summoned to Cameron's office, The Guardian reported.
While the moves have not been announced, Cheryl Gillan, the secretary of state for Wales, removed that job from her Twitter profile.
The reshuffle is the first since the Conservative-Liberal Democratic coalition took power in 2010. It is also expected to be the last before the next election in 2015.
Cameron is expected to leave those in the top positions where they are, including George Osborne, the unpopular chancellor of the exchequer, the Financial Times reported. Foreign Secretary William Hague, Home Secretary Theresa May and Education Secretary Michael Gove are also expected to stay.
The casualties are expected to include Justine Greening, the transport secretary, Culture Secretary Jeremy Hunt, Health Secretary Andrew Lansley and Environment Secretary Caroline Spelman. Hunt embarrassed the government with his handling of Rupert Murdoch's attempted acquisition of BSkyB and Spelman with a much-criticized plan to privatize national forests.
"The prime minister sees the second half of this Parliament as the delivery phase," a source in the government told The Guardian. "We want to have people who have a proven record in delivering in their departments."
The prime minister's office confirmed Andrew Mitchell, an Osborne ally, will move from international development secretary to chief whip, The Guardian said. He will replace Patrick McLoughlin, a former miner, who will be moved into the Cabinet to give a more public role to someone from a working-class family.
Justice Secretary Kenneth Clarke, who has been fighting to keep his job, is expected to be demoted, the Financial Times reported. Sayeeda Warsi, who sits in the House of Lords and serves as Conservative Party co-chair and minister without portfolio, is also likely to be axed.
Wisconsin business offering 'therapeutic cuddling' forced to close
Ohio crash that killed two caught on camera [VIDEO]