After losing Nemanja Matic, Antonio Conte is keen to bring in Danny Drinkwater to provide competition in midfield.
Talks between the two clubs over a £30 million deal have already begun with the player willing to make the switch to Stamford Bridge, but Shakespeare is reluctant to sell.
‘We don’t want to be a selling club, we want to add to it. We don’t want to sell our best players. The speculation is always going to be out there at this time of year', the Leicester boss said.
‘You know when you have good players there might be an interest in them. You have to deal with reality but also keep a calmness about you as well', he added.
Drinkwater is currently sidelined due to a thigh injury and will miss the Foxes' Premier League opener against Arsenal.