Sky News has learnt that Elliott Advisors, which has backed a string of UK retail deals, is one of a small number of bidders to have lodged formal offers for the chain.
A source said that Elliott had been granted a short period of exclusivity within which to conclude negotiations about a deal.
If the talks do result in a transaction, it would see Waterstones changing ownership for the first time since 2011, when the Russian billionaire Alexander Mamut snapped it up from the ailing entertainment retailer HMV Group.
The price tag being discussed was unclear on Monday, although one insider suggested it was likely to be much lower than the £250m that a newspaper report said Mr Mamut was seeking last autumn.
Mr Mamut has been seeking to raise cash following a crisis at Otkritie, a Russian bank where he is among the biggest shareholders.
Elliott Advisors is part of a bigger investment management empire which is best known for taking aggressive activist positions in a string of major public companies.