He insists the club have no intention of selling the 23-year-old Bosnian who reportedly refused to play in the Carling Cup match against Shrewsbury in midweek after being linked with the Premier League champions.
Stoke signed Begovic from Portsmouth and Coates said: "I felt huge disappointment. He's an exceptional young goalkeeper, one of the best in the country.
"Clubs like Chelsea make enquiries about them and their heads can get turned very easily. It's just bad advice they get given, they shouldn't listen to it but obviously they do."
When asked on BBC Radio Five Live's Sportsweek programme if Begovic might move to Stamford Bridge before the transfer window closes, Coates added: "I know nothing about it. I would say the answer is no.
"We're in a difficult position here. We just can't go out and find a goalkeeper, they're very hard to find."
Reports have suggested Chelsea were prepared to bid £4.5million.
Coates said: "You may have heard a rumour and it may be pretty good information, but the fact is we've rejected any offer they've made. They made an enquiry and they did make an offer and it was rejected."
Asked if a bigger offer might tempt Stoke to sell, Coates said: "Silly offers do have an effect on you but nothing like that has happened and we're not expecting it to happen and our position is we see him remaining our goalkeeper."