The Potters chief believes the Bosnian keeper is among the best in the Premier League, and thinks his side need to be realistic if a big-money offer comes in amid reported interest from City and United.
"I feel he's as good as anybody in the Premier League," Coates told The Sentinel, as reported by the Manchester Evening News.
"I don't know anyone who is better. You always have to be realistic about these things. If a call came from a top European club and was attractive to him, then you have to look at it.
"It wouldn't be much of a surprise to me and that's why we have contingency plans in place with other goalkeepers at the club."
Stoke signed England under-21 shot-stopper Jack Butland over the summer, and the highly regarded keeper is currently on loan in the Championship with Barnsley. Thomas Sorensen is Begovic's back-up at the Britannia Stadium.
With replacements already secured, Stoke may consider offers from the likes of City and United for the 26-year-old Begovic.
"We would be reluctant to sell him because you want to keep your best players, but equally you are realistic about things," Coates continued. "You also have to consider the player's view."
United and City are not the only clubs mentioned as possible suitors for the Stoke stopper - Atletico Madrid and Napoli have both been linked with Begovic in recent months.