The defender has enjoyed a sensational first full season for the Scottish Premiership side.
The 18-year-old has just enjoyed his first full season as part of the Hoops' first-team but took little time to establish himself as the side's first-choice left-back.
His form for the Bhoys this past campaign was perhaps only bettered by Leigh Griffiths, and has therefore, unsurprisingly caught the eye of several Premier League sides, including Arsenal, Manchester City and Liverpool, the Record claims.
But it is Arsene Wenger that appears to be leading the way to bag his signature after he sent Steve Rowley to have a closer look at the defender as he weighed up a potential switch.
And with the Record reporting that the feedback was extremely positive regarding the youngster's potential, it appears that the North London side will look to bring him to the Emirates this summer, and are prepared to offer as much as £10m to land him.
With the Hoops having had to watch several of their key men depart Parkhead for England in recent seasons, it seems likely that they will have a plan in place and targets lined up should Tierney depart in the coming months.
Nevertheless, the promise he has shown since coming into the side would make his exit a huge blow to the new manager as he tries to put together a team capable of winning the Scottish Premiership for a sixth year in a row.