CSC has NHS IT contracts worth about £3.2bn, as a local service provider under the NPfIT.
The question comes as the CIO for Health, Christine Connelly, with officials and lawyers at the Department Health, seek to negotiate a memorandum of understanding with CSC after it missed deadlines to install the iSoft "Lorenzo" software at NHS trusts.
Conservative MP Richard Bacon, a member of the Public Accounts Committee will ask the question. He is concerned that the DH's new deal with CSC would greatly increase the cost to taxpayers of each Lorenzo installation.
He is due to ask Cameron:
"What discussions he has had with the Minister for the Cabinet Office and the Secretary of State for Health on the performance of Computer Sciences Corporation in installing Lorenzo software within the National Programme for IT in the NHS."
In April Bacon wrote to Cameron asking that he insists that Connecting for Health "accepts the need for full and unhampered Cabinet Office involvement in the [CSC] renegotiation process".
Bacon is concerned that Connecting for Health is unwilling to involve the Cabinet Office in matters relating to NHS IT contracts - although the Cabinet Office has a mandate from Downing Street to oversee major government contracts, especially those with a large IT component.
The signs so far are that CfH has managed to stay outside of the Cabinet Office's spending controls. The NPfIT programme, also, has been largely unaffected by the coalition's coming to power, despite publicity that the NPfIT is coming to an end.
The Health Secretary Andrew Lansley and NPfIT minister Simon Burns appear to have decided to leave the NPfIT to their civil servants.