The 29-year-old is in the final year of his contract and is keen to move to the Premier League with Wolves and Nottingham Forest competing against the Cottagers for his signature.
Marco Silva has tasked Fulham with adding attackers to his squad before the transfer window closes on September 1 and is interested in Hwang as he can also play in wide areas.
After seeing the club add several central defenders in the last week, the Portuguese manager has now instructed the likes of Tony Khan and Alistair Macintosh, who work on transfers, to conduct further business.
As well as moving for Hwang, the club are in advanced negotiations with Roma winger Justin Kluivert and are also in talks with Bayern Munich's Joshua Zirkzee.
German side Stuttgart have recently emerged as competitors for the signature of Zirkzee. Several sources have also moved to deny rumours of advanced talks between Fulham and former Chelsea and Arsenal winger Willian, who has cancelled his contract at Corinthians in order to return to European football.