Tierney has enjoyed a fine season at Celtic.
The left-back has caught the eye with a series of impressive displays, helping the Hoops open up a 25 point lead at the top of the Scottish Premiership.
Reports earlier this month claimed Arsenal were considering a summer bid for the 19-year-old.
Stars who have played in both Scottish and English Premier Leagues
Fri, April 15, 2016
Express Sport takes a look at some of the greatest players who have appeared in both the English and Scottish top flights in recent times
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Express Sport takes a look at some of the greatest players who have played in both the Premier League and the Scottish Premier League (now Scottish Premiership)
Celtic star Kieran Tierney is wanted by Manchester United
Kieran Tierney is already a Scotland international at 19
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Head scout Marcel Bout watched Tierney in action in Celtic’s 1-1 draw with Rangers on March 12.
United chiefs were also impressed by his performance in the 3-3 draw with Manchester City back in September.
Jose Mourinho is eying a new full-back with Luke Shaw and Matteo Darmian’s futures in doubt.
Shaw has struggled for game time under Mourinho, while Darmian has flitted in and out of the side.
Moussa Dembele is also on Manchester United's radar
Celtic will demand a fee of £10million to part with their star asset.
And the Hoops also face a battle to keep hold of star striker Moussa Dembele.
Dembele has scored 32 goals for Celtic this season and a host of top clubs are keen to lure him away from the Scottish capital.
Chelsea tried to sign him in January – and the player has since turned down a move – but Dembele is also wanted at Old Trafford.