The 19-year-old defender will be out of contract in the summer and has been weighing up his options over his future.
Sheffield Wednesday are hoping to see him sign a new contract and his representatives have been in talks with the Championship club over Shaw staying at Hillsborough.
But Shaw is also considering offers from other clubs and Celtic are keen to snare him away from Sheffield Wednesday when his deal runs out.
And it has been claimed that negotiations are under way between Shaw’s camp and the Glasgow giants over the defender moving to Celtic Park.
The Bhoys are hoping to lure the talented prospect away from Wednesday and would only have to pay a paltry compensation to the Championship club.
Clubs from outside England are free to discuss a pre-contract with Shaw, but English outfits can only hold talks later in the year.
However, the young midfielder has not taken a call on his future and is in no rush to make a decision at this juncture.
The 19-year-old is keen to consider all the offers on his table before deciding whether to stay at Sheffield Wednesday or move to another club.
