The concept, which was founded in 2015 by Fabian Clark, is understood to be close to securing the former clothes shop unit at 21 Kingly Street for an opening later this year.
Earlier this year it opened a site at the fishing container scheme in Broadgate Circle.
Over the last two years CLAW has operated at markets throughout London, festivals across the UK and pop-ups at various restaurants and bars.
Clark believes crab is undervalued in the UK with approximately 80% of the country’s catch sold internationally.
As the name suggests CLAW specialises in competitively priced crab and lobster brioche rolls. The menu currently includes a crab roll with baby gem and lemon mayonnaise; a lobster and crayfish roll with sesame mayonnaise; and a poke roll with diced Hampshire trout and horseradish crème fraîche.
Davis Coffer Lyons is believed to have acted on the Kingly Street deal.