According to the 'BBC', the Madrid club are expected to send scouts to the Scottish Cup final as Celtic take on Motherwell, before making any decisions regarding a bid for the defender.
Tierney has been a regular starting feature in the Celtic squad since 2015, and has earnt nine caps at international level representing Scotland.
The 20-year-old has claimed three Scottish Premiership titles at Celtic, as well as the PFA Scotland's Young Player of the Year for the third consecutive season.
Given the injuries to Atletico's defence this season, Tierney would be a great addition in terms of depth due to his versatility.