Begovic has been linked with interest from Arsenal and Manchester United, but Hughes is desperate to keep the Bosnia-Herzegovina international at the Britannia Stadium for as long as possible.
Speaking after Begovic kept his third top-flight clean sheet of the season in Saturday's 0-0 draw with West Brom, Hughes told reporters: "We've got one of the top keepers in Europe.
"When he goes to the World Cup, he might prove he's one of the best in the world. I'd like to work with Asmir for many, many seasons because I think he's that good.
"He's had a great week - qualifying for the World Cup and putting in an outstanding performance for us."
Hughes, who has made 101 Premier League appearances for Stoke, has 32 months remaining on his current contract.