The South Korea international spent the 2013/14 campaign on loan at Sunderland after being deemed surplus to requirements in South Wales.
Gus Poyet expressed an interest in making that deal permanent midway through the season, but transfer talk cooled after Ki’s form dipped over the final few weeks.
He is now expected back at the Liberty Stadium this summer as he still has a year left to run on his current deal.
Monk is prepared to offer the midfielder a clean slate, with his predecessor Michael Laudrup having taken the decision to move him out, and has refused to rule out the possibility of fresh terms being tabled if the former Celtic man impresses.
He told the South Wales Evening Post: “I think Ki is a quality player and, as things stand, he will be with us next season.
“Ki can add quality to our squad, he proved that with his performances at Sunderland last season.
“If he is with us next season and he plays and he does well, we will then look at extending his contract.”