In an interview with London newspaper City AM, co-founder Will Beckett said the currently 13-strong group hopes to go from opening one or two restaurants a year to between two and three.
The group has been growing steadily since the first Hawksmoor was launched on the Eastern edge of The City in 2006. In recent years, it has opened around one restaurant per year.
Beckett says that Hawksmoor is focused on the US - where it already has two restaurants in New York and Chicago - but would not rule out opening further restaurants in the UK and exporting the brand to other countries should the right opportunities come up.
“The US is where the majority of our attention is,” he said.
In July, it was revealed that Hawksmoor had been put up for sale in a deal that could value the restaurant chain at about £100m.
As first reported by the FT, investment bank Stephens has been hired to run a sales process and begun speaking to potential buyers.
London-based private equity firm Graphite Capital invested £35m for a stake in Hawksmoor in 2013, and has owned 51% of the business since then.
According to the FT, Beckett and fellow co-founder Huw Gott, who own a minority stake, will retain their shareholding to continue to lead the company following the sale.
In the interview with City AM, Beckett confirmed that the process of finding a suitable buyer for the group was under way but was “not at fruition yet”.