Wilson, 23, captained Hearts to the Scottish Championship title but chose to invoke a clause in his contract which allowed him to leave the club on a free transfer this summer.
Bhoys manager Ronny Deila told Sky Sports earlier this year that he was interested in handing former Rangers centre back Wilson a return to Glasgow - but the Daily Record believe that Celtic have now ended their interest in the defender.
Having already signed Manchester City's Dedryck Boyata this summer, it seems that the Bhoys have pulled out of the race to sign Wilson - leaving him free to join former club Rangers.
A report from The Sun earlier this week suggested that Rangers had already held talks with Wilson over a shock return to Ibrox, five years since he left the club for Liverpool.
The Daily Record believe that Celtic pulling out of the race means that a move back to Ibrox is on the cards, and he could form a partnership with Wigan's Rob Kiernan, who is on his way to Rangers according to STV.
Kiernan and Wilson - a promising partnership?
After witnessing poor displays from the likes of Lee McCulloch and Bilel Mohsni last season, Rangers could have a partnership for years to come in Kiernan and Wilson.
Kiernan, 24, and 23-year-old Wilson still have plenty of potential to grow at Rangers, giving new manager Mark Warburton a more youthful defence for the coming season.
That should be music to the ears of Rangers fans, who saw the 'experienced pro's' fail badly in the 2014/15 season, with Warburton now looking for players who can perform right away but still have potential to become even better under his tutelage.