The Edinburgh club made an approach to sign Lee now in time for their European campaign starting. However his club, Suwon FC, are reluctant to sell their talisman in the middle of the K League 1 season.
The player is out of contract later this year and Hearts hope a pre-contract offer could tempt him to Scotland. Should their move be successful, he would be registered once the January transfer window opens.
Other clubs in Europe and Asia are also keen to sign Lee, who operates as a left winger or second striker. He has scored ten goals in 22 appearances for Suwon so far this season and is currently serving a domestic suspension.
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How the Hearts players rated in the draw against Hibs
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Suwon are doing everything possible to keep the 24-year-old and Hearts are aware their prospects of signing him in the current transfer window are dwindling. A pre-contract offer would remove the need for any approval from Suwon if Lee is willing to continue his career at Tynecastle Park.
A three-year deal is on offer should he decide that the Scottish Premiership is his next career destination. Hearts believe the forward would add pace, creativity and a scoring instinct to their attack.
Lee is a graduate of Barcelona’s La Masia youth academy and played for the club’s B team before joining the Italian side Hellas Verona for €1.5million in 2017. Two years later he moved on to Belgium with Sint-Truiden.
After a loan spell at the Portuguese club Portimonense – where he was coached by former Hearts manager Paulo Sergio – Lee returned to his homeland to rejuvenate his career with Suwon earlier this year.