The dispute centres on objections from some quarters that the vertical curves of Sir Norman's designs for the City offices give the buildings undue prominence over the surrounding area.
The controversy comes in the week that Sir Norman's reconstructed Reichstag building was opened in Berlin,
On Tuesday, City aldermen will vote on whether to approve the two massive schemes in London Wall, in the heart of the Square Mile.
It is understood that the smaller one, at 289,000sq ft will not be modified, as it is on a curved site. But a senior City source said that the design of Moor House, a 480,000sq ft office developed by Greycoat, could "draw undue attention to the building".
Meanwhile, property company Minerva has commissioned Sir Norman to design a 450,000sq ft building near Mansion House, which will come before City planners within two months. Again, the building features a "vertical curve". Observers said that a solution would be to place the building in a transparent box to mitigate its impact.
A spokeswoman at Sir Norman's practice refused to comment on the City's suggestion or the row.
Sir Norman's plans for a Swiss Re tower at the Baltic Exchange site, which was bombed by the IRA in 1992, will be submitted within six weeks.
However, drawings of what will be the second tallest building in the Square Mile have already been criticised by some in the City.Reuse content