BBC Sport report that the Europa League finalists are interested in adding Tierney to their ranks, but the club wishes to cast an eye over him first in the clash with Motherwell.
The news will come as a blow for Manchester United and Tottenham, both of whom are believed to be tracking Tierney. With Atletico potentially entering the race, the Premier League rivals may have to step up their interest in the Scottish starlet.
Tierney has been a mainstay in the Celtic side since 2015, helping his side to three consecutive titles and two Scottish Cups. His performances have brought him much acclaim in the Scottish Premier League, winning young player of the year three years running.
He has already won nine senior caps for the Scottish national team and was also named in the SPL Team of the Year for the past two seasons.
Atletico are second in La Liga and need just a point in their final game against Eibar to secure a finish above bitter rivals Real Madrid. The Spanish club are also in action Wednesday night where they will face Marseille in the Europa League final.
Atletico have plenty to offer the 20-year-old left-back who is beginning to look set to depart Celtic this summer. He is under contract until 2023 with the Scottish champions though, so they will have plenty of sticking power during negotiations over a fee.
Tierney and Celtic take on Motherwell on Saturday where Brendan Rodgers side hope to complete a successive domestic treble as they continue to dominate the Scottish top flight.