Permission has been sought to demolish Federation Square's Yarra Building to make way for a controversial new Apple store, sparking accusations the process is being rushed to avoid scrutiny.

Image of the new Apple store at Federation Square, included in a Melbourne City Council planning report.

The square's management has applied for a heritage permit to knock down part of the large postmodern building, arguing in a 124-page impact statement that it is not of the same design standard as others in the precinct.

The plan to replace building with the tech giant's flagship store – one of only five in the world – has been met with a torrent of public criticism since the Andrews government confirmed the deal in 2017.

Federation Square is in the process of being considered for addition to the state's heritage register.