Out of contract at the end of 2024, Kelly is now attracting strong interest from Bundesliga giants Bayer Leverkusen and RB Leipzig as well as clubs in England.
Football Scotland understands both parties are still far apart in negotiations and talks will continue as nothing has been agreed.
With his contract expiring at the end of this season Celtic could take away some of the concerns by adding 12 months onto his current deal to eliminate that issue from his thoughts.