The 18-year-old's current deal expires at the end of the season, and the club are keen on extending his stay at Celtic Park.
Kidd is yet to make his senior debut for the Bhoys, but he has followed up from a very impressive Next Gen tournament last year to shine in their current Youth Champions League campaign.
Kidd is a natural midfielder, but he has been used extensively at right-back this season - where he impressed and his displays have attracted interest from other clubs.
Ajax were linked and it is also claimed that their Dutch rivals FC Twente are keen, whilst Premier League outfits Sunderland and Aston Villa are also said to be monitoring the situation.
A source told Sky Sports: "Lewis's situation is something numerous clubs will be actively looking at.
"He has performed well so far for Celtic this season and looks like he can go all the way."