Goal.com revealed last week that Liverpool are leading the race to capture the 19-year-old England international, while Everton manager David Moyes recently admitted that his club have made enquiries in the past.
Southampton are believed to have had a bid of around £6 million rejected in the summer transfer window and Clark insists that Premier League sides will need to improve their offers to tempt the Blues into a sale.
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"We would be looking for an even more substantial figure than we were offered in the summer - even though I certainly don't want it to come to that."
Birmingham have struggled so far this season and currently lie in 19th place in the Championship as the season approaches its halfway point.
Clark hopes to be allowed to construct a brighter future around the likes of Butland, but admitted that the club's executives would have the final say on bids received in January.
"Ultimately, it's down to the board," he added. "He's the future and the type of player I'd rather build my team around."