director Simon Allford told that the studio is no longer involved in the £650 million scheme at London's King's Cross, despite working on the project for over three years.
It will now be planned by the firms of Bjarke Ingels and Thomas Heatherwick, who are also working on the company's new California headquarters.
But Allford insists his firm's relationship with Google is still good, and claims to be working on other projects with the tech giant.
"We are not going to do [the job]," Allford told BD. "We have a tremendous relationship with Google London and we are doing a £100 million project for them on a BNP Paribas building."
AHMM won planning permission in 2013 for its first Google London proposal – a steel-framed 11-storey structure with primary colours picked out on the facade. But Google later asked the firm to scrap the plans and come up with something "more ambitious".
The firm added numerous features, reportedly including a swimming pool and running track on the roof, and a docking station for airships.
Despite this, CEO Larry Page allegedly branded the scheme "boring". Heatherwick and Ingels were subsequently drafted in, following the positive response to their innovative Mountain View scheme, which will be built by robots.
Originally scheduled to open in 2017, the headquarters will allow Google to consolidate its London operations under one roof.
It will replace existing offices in Covent Garden and Victoria on a site that stretches 330 metres from Regent's Canal towards King's Cross station, alongside another planned Google office building by Mossessian Architecture.
London-based AHMM is led by Allford with Jonathan Hall, Paul Monaghan and Peter Morris. Past projects include a hospice designed to look like a big house, and the firm is also working on the new Scotland Yard headquarters.