The 21-year-old has only been on the Swiss club's books since January this year, but has scored an impressive 14 goals from 22 appearances, plus six assists.
According to Sky Sports News, the newly-promoted Gulls have been keeping tabs on Dwamena, who joined Zurich from second-tier Austrian club Lustenau, but it has been turned down.
Zurich president Ancillo Caneta is quoted by Ghanasoccernet as saying: "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.
"Sure, when a certain scale is reached, you have to do the business as a Swiss club for economic reasons. So I do not want to exclude a sale, but so far there is no offer at a financial level where I would be nervous. We have no economic need to surrender to Dwamena."
Brighton manager Chris Hughton has already signed seven players during the transfer window as his charges prepare to take part in the 2017-18 Premier League season.