Schroders is under offer to buy 55 Bishopsgate, EC2, from Canada Pension Plan Investment Board for more than £185m.
The fund manager is understood to be acting on behalf of an overseas investor with whom it has a separate account mandate.
CPPIB instructed CBRE to find a buyer for the building at the start of this year seeking bids of £170m – a c4.75% yield.
China Minsheng entered discussions to buy the building for around £180m this summer but no deal was agreed.
CPPIB bought the building in 2006.