The Daily Mirror is reporting that Manchester United have held a long-standing interest in the Scottish prospect.
The same article states that the Red Devils were previously looking at a potential swoop to sign Tottenham’s England international Rose.
However, Tierney is able to play across a variety of positions in defence unlike Rose, who is predominantly a left-back.
According to the same story, Manchester United are ready to step up their interest in Tierney but Celtic are likely to demand a transfer fee in the region of £25m.
The 20-year-old has already amassed nine caps for the Scotland national team following an impressive start to his Celtic career.
Tierney scored six times in 120 appearances in all competitions over the past four seasons to establish himself as one of British football’s most-exciting prospects.
Manchester United manager Jose Mourinho has used Luke Shaw sparingly since his appointment as Louis van Gaal’s successor in May 2016.
Indeed, the Portuguese coach has been critical of the England international’s poor performances.
The Red Devils are in second place in the Premier League table but 16 points adrift of leaders Manchester City.
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