The 25-year-old is currently with the Latics and manager Steve Bruce could make a move to sign the player next week.
Any deal would be able to go through outside of the transfer window as the 27-cap international is a free agent after his contract with Korean club Suwon Bluewings expired.
The midfielder has impressed Bruce both on and off the field during his brief time at the club and he would give the former Birmingham boss more options going into the season's run-in.
"Won Hee has come and trained with us for the past couple of days and has done really well," Bruce said.
"We have been really impressed with him as a player and a person and can sign him as he is not under contract with any club."