Today's Mail on Sunday claims that benefactors are also promised they will be kept close to policy developments and will even get the chance to chat with him after Prime Minister's Questions.
The MoS says the offer to meet Mr Cameron is contained in a Tory leaflet sent out to well-heeled supporters and distributed at a meeting last week of the City Circle, a group of financiers who help to bankroll the party.
It says the meetings are one of the benefits of being in the so-called "Leader's Group" - for an annual membership fee of £50,000.
MPs are accusing Mr Cameron of abusing his position.
LibDem rotweiller Norman Baker said he would be asking the Serjeant at Arms to investigate. He added:
Mr Cameron's office, like those of other MPs, is paid for by the taxpayer to perform a public function - not as a fundraising venue for the Conservative Party.A spokesman for the Serjeant at Arms, who is charged with ensuring that MPs observe the rules and traditions of the House, told the MoS he was "unsure" if there was any guidance that banned the use of offices there for party fundraising.
If it isn't against the letter of the law, then it is certainly against the spirit. Selling access to Mr Cameron's office is an abuse of the House of Commons and represents a return to the Tory years of sleaze.
MPs are banned from using the Commons' private dining rooms "for direct financial or material gain by a sponsor, political party, or any other person or outside organisation."
The Conservatives have denied breaking the rules.
Even so, the controversy comes at the end of a bad week for Cameron when he was trying to celebrate his first anniversary as Conservative Leader:
Last weekend, he was accused of involvement in a Tory scam to use the private dining rooms at the Houses of Parliament for political fundraising events.
Then, on the day of his first anniversary, one of his parliamentary candidates in a marginal seat quit, claiming a senior party officer had made disparaging comments about disabled people.
And yesterday, I reported on the defection of a senior Tory activist to UKIP and a sharp rise in the number of Tories who were dissatisfied with Cameron's leadership.