The leases on the sites, which include such prime locations as Haymarket, Leicester Square and Oxford Street, are being marketed for £5m.
Mike Gilbert of Hammond Phillips, which advises Burger King in the UK, said the company had registered its interest with the agentr acting for Aberdeen Steak.
Gilbert said: "Clearly there are some good sites. It's very early days but we are treating it very seriously.
"It's unlikely we would go for the whole lot. On the other hand, it's difficult to get units like these with A3 consent, so we wouldn't rule anything out."
Several restaurants and pub groups have contacted Aberdeen's agent, and observers expect the sites to be cherrypicked by a mixture of independent restaurants. McDonald's has not ruled itself out as a possible bidder, though it said it already had a good pesence in the West End. Some potential bidders have said they were put off by the high rents and big premiums being asked.
Aberdeen's owner, Ali Salih, is still trying to put together emergency finance to rescue the group. Salih put the group into administration a fortnight ago after it suffered from the downturn in tourism to the West End of London. Shay Bannon of BDO Stoy Haward, the administrator, said the alternative was to sell the business to a third party without the current management.