It is understood the city council has been engaged in 'high-level' conversations with EH after the agency recommended the 14-storey Modernist office block was given Grade-II listed status - a move the authority feels could scupper city-centre regeneration (AJ 28/06/07).
And in the last few days, outraged local campaigners 'baffled' by the decision, have set up an online petition to try to provoke a rethink by the Department of Culture Media and Sport, which approved the listing.
It is also argued that maintaining the listed building will cost more than £40 million and 'has the potential to bankrupt the council'.
However, The Twentieth Century Society (C20), which put the building forward for listing, has launched a robust defence of the decision, claiming that the interiors in particular are worth saving (pictured).
In a letter to the local press, C20 caseworker Jon Wright said: 'It is the society's firm belief that this building was, and still has the potential to be, a symbol of Plymouth's civic and municipal pride.
'Built as an expression of the creativity and sheer will that saw Plymouth resurrect itself after World War Two, the centre remains a tribute to the pioneering spirit of that time and the society is pleased to note that English Heritage made specific reference to this in the list description.'
Wright goes on to say that there are other, wider issues at stake: '[This is more] than a simple vote on whether a building is ugly or not and should be knocked down.
'If we had acted on those impulses in the past, many great buildings which we rightly see as important now would have been lost long ago.'
He added: 'In addition, we are starting to understand the importance of a sustainable approach to suit the changing needs of our towns and cities. Knocking down perfectly good buildings and replacing them is something we simply cannot afford to do any more.'
Intriguingly, an e-petition has gone up today asking people to sign up to show their support for the listing.