Our sister paper The Sheffield Star reports the Hoops are looking to convince the 19-year-old his future lies away from Hillsborough with preliminary discussions underway.
The English Championship club haven’t given up hope of convincing the player to extend his current deal, which is set to expire this summer. Shaw is said to be open to the idea of signing a new deal but is keeping his options open and could be tempted by the prospect of playing European football.
The versatile academy graduate emerged for the Owls this season, making 12 appearances in both competitions while sharing time at centre-back and centre-midfield.
Celtic would only have to pay a cross-border compensation fee for the player, who recently scored his first goal for Wednesday in a 2-1 victory over Middlesbrough.