The South Korean international (below) has attracted attention from Blackburn Rovers and Spurs, with the Parkhead club dismissive of any moves for the player. There has also been interest from Russia.
However, it would take a bid of significant proportions for Celtic to allow the increasingly important midfielder to leave the club.
Ki was on the scoresheet as Celtic beat Dundee United 5-1 and his recent performances have seen him attract interest, but Neil Lennon regards the 22-year-old as an intrinsic part of his midfield and would not welcome any interest.
Meanwhile, Celtic's hunt for a goalkeeper has re-alerted them to the situation of Scotland international Craig Gordon.
He has recovered from surgery earlier than anticipated and is expected to start training with Sunderland this week.
With Keiren Westwood and Simon Mignolet already ahead of Gordon at Sunderland, a loan move could appeal to both the player and Celtic.
However, his £40,000-a-week salary is a potential stumbling block.
Celtic had been keen to sign Polish keeper Grzegorz Sandomierski, but the player finally signed for Genk on Friday evening and Lennon remains desperate to bring in another shot-stopper.
Meanwhile, Liverpool are rumoured to be keeping tabs on Paddy McCourt.
At Lennoxtown, Lennon will take a look at Moenchengladbach striker Mo Idrissou.
The Cameroon internationalist, 31, has 32 caps but has become a fringe player in the Bundesliga and is available for around £700,000.