Arnold will remain in charge of the Socceroos and Olyroos, with his agent Tony Rallis confirming the 57-year-old had knocked back the Korean club's offer.
"He's rejected it," Rallis said on Wednesday. "It was a great offer but it just sprung up on him."
On Tuesday, FFA chief executive James Johnson said he wasn't surprised Arnold was receiving interest, but expected the Socceroos coach to remain at his post.
"The prestige of coaching a national team is a rare opportunity and we would expect that Graham Arnold sees through his commitment as national team coach of Australia as we continue our path towards the FIFA World Cup in Qatar in 2022," Johnson said.
Arnold hasn't led the Socceroos in a game since November last year, with World Cup qualifiers and a maiden Copa America appearance scuppered by COVID-19 while the Tokyo Olympics were postponed until 2021.
Australia had enjoyed an unbeaten start to their qualification campaign for the 2022 World Cup, while Arnold also secured the Olyroos qualification for the Olympics for the first time since 2008 with a third-place finish at January's AFC Under-23 Championship.
Arnold officially took the reins as Socceroos coach after the 2018 World Cup, signing a four-year deal through to the end of the 2022 tournament in Qatar.