The former aide to Tony Blair resigned last week and is believed to be teaming up with Darren Murphy, who quit APCO in the summer to set up a political comms agency.
Rahman joined APCO in 2007, having previously spent seven years as assistant political secretary to Blair at 10 Downing Street.
His resignation comes within weeks of the departure of Murphy, head of APCO's global services to government division and another former Blair aide.
Murphy is teaming up with ex-Number 10 colleagues to set up a political comms agency called Centreground Political Communications. It is understood that Murphy, an ardent Blairite, plans to link up with former colleagues who share his political outlook.
Rahman and APCO declined to comment, but well-placed sources suggested he would help Murphy to run the new operation.
Rahman joined APCO in 2007 as an associate director. He was the first Downing Street adviser to move into public affairs following Blair's resignation. At the time, Murphy was said to have lured him to APCO.
While at Number 10, Rahman was responsible for advising the prime minister on political, policy, legislative and Labour Party matters.
In 2005, Rahman narrowly missed out on being selected as the Labour candidate for the safe seat of Brent South.