The 26-storey office block was sold, along with the stock exchange market building and the former post office building on Throgmorton Street, to developer Hammerson for £67m last week. The site came with planning permission for a scheme designed by Grimshaw.
However, market sources said Hammerson may consider using another architect. One pointed to the fact that it had not worked with Grimshaw before.
The source said: "Grimshaw is one of a number of candidates for the job. There are others around."
Another said the timing of the scheme was uncertain, as it depended on "the scope of the project, the specification and the state of the office market".
The construction cost of the project, which will include recladding, refurbishing and extending the tower, is likely to be about £100m.
The stock exchange, which put the building up for sale last October, received planning permission for the facelift in April last year.
The Hammerson purchase comes amid an upturn in the office market in central London, with a batch of office projects expected to be commissioned at the end of this year or the start of next.
The Old Broad Street scheme includes 50,000 m2 of offices and 2800 m2 of shops, and will include two additional office blocks. The exchange is moving to King Edward's Court in Paternoster Square, near St Paul's cathedral.