The committee wants to grill former Downing Street aide Murphy about his transition from Number 10 to public affairs.
He has been called to appear before the committee on 8 May, along with former health minister Lord Warner and ABI director general Stephen Haddrill.
A spokeswoman for the committee said it wanted to investigate 'how the appointment rules work when someone moves from government to business'.
It will consider how best to police the 'revolving doors' of politics and business, and whether tougher rules are needed.
Murphy joined APCO in 2005 after three years at Number 10, first as assistant political secretary to prime minister Tony Blair, and then as Blair's special adviser on political communications.
Warner, a former adviser to Jack Straw, was a minister at the Department for Health from 2003 to 2006. He is now employed by DLA Piper to provide advice to the law firm and its lobbying practice.
Haddrill was made director general of the Association of British Insurers in 2005, having previously held a number of senior civil service roles.
These included three years as director general of the fair markets group at the then Department of Trade and Industry.
The select committee plans to hold a further two final sessions in May, with witnesses yet to be decided as PRWeek went to press.