The Potters snapped up Birmingham City shot-stopper Jack Butland, who will finish the rest of the season on loan at St Andrew's, last month.
Following the transfer, Begovic, who is thought to have been targeted by Premier League title chasers Manchester City and Manchester United, is under no illusions that he will be first-choice keeper at the Britannia Stadium by the time of the new campaign.
"I read in the papers that I said no to City and yes to United, but the truth is, I haven't decided on anything," Sky Sports News quotes Begovic as saying.
"I didn't say yes or no to anybody. I haven't signed anything, no contract, no pre-contract. But I believe that Stoke didn't buy Butland to be a reserve so I think I'm going to be sold in the summer.
"To whom? I can't move to a smaller club and I also know that some top clubs are interested in me. They are also the only ones who can afford the fee."
Recent reports have claimed that United will clinch the goalkeeper's signature for a £9m fee.