Brighton are interested in signing the Ghana international, who joined Zurich from RB Salzburg, but their first bid of £8m has been rejected. Dwamena helped his team to promotion last season by scoring twelve goals in 18 games.
"We've always had inquiries for him on the table, and yes, we currently have an offer from England but we do not want to sell him for sporting reasons," Zurich President Canepa said.
So far, Brighton have signed seven players in this summer's transfer window.