The 22-year-old is currently representing his country at the Asian Cup in the United Arab Emirates where he has scored two goals during his side's passage to the last 16.
But he could yet seal a move to the Premier League over the next few days, with his current club, Jeonbuk Hyundai Motors, confirming an offer - reported to be in the region of £6 million ($7.7m) - has been received from the Hornets.
"Watford have made an offer," revealed general manager Baek Seung-kwon to SPOTV News. "I cannot give many details about the deal, but it will be like how Lee Jae-sung [who joined Holsten Kiel in July] went to Germany.
"Kim also knows that Watford’s proposal has come in. The player and Watford are in negotiations and he is doing it through his own channels because he is away at the Asian Cup."
Nicknamed 'Monster', Kim has been likened in his home country to England defender Harry Maguire due to his strong physical presence and threat from set-pieces.
He has won 15 caps for South Korea, though he missed out on the 2018 World Cup with a back injury, and has previously held talks with Chinese Super League side Beijing Guoan regarding a transfer.
He has now recovered, however, and will line up in a team set to contain Tottenham forward Son Heung-min when South Korea take on Bahrain on Tuesday.
Should he complete a move to Vicarage Road he would battle with the likes of Christian Kabasele and Craig Cathcart for a place in Gracia's first team.
The Spanish coach has earned praise this season, with his side sat seventh in the table heading into the Premier League weekend.