The former home of the Sun, Times and Sunday Times is one of the biggest development opportunities in London.
It is understood that the Tony Pidgley’s business has offered around £150m for the 15-acre site, according to a report in the FT.
News International came close to selling the 15-acre site three years ago for around £200m to property developer Marcus Cooper, but a deal was scuppered by the property collapse.
More recently News International toyed with its own plan to redevelop its Wapping headquarters but ditched the idea last September.
During the 12 months, Berkeley has bought 15 sites in the London and South East.
A deal would give Berkeley top a slew of big London sites along the Thames from Kew to Battersea, Blackfriars, Tower Bridge and Wapping.