Tierney was named as the Scottish Football Writers’ Association’s Young Player of the Year after another impressive campaign for Celtic.
The 20-year-old has been heavily linked with Manchester United in the past, while Sky Sports claims Bournemouth have made him their priority left-back target this summer.
Spotted by the BBC’s gossip column, the Express’ print edition ran a story on Thursday suggesting Spurs could test Celtic’s resolve with a £20 million bid.
There is a chance Tottenham will be in need of a new left-back for next season if Danny Rose departs as he is expected to.
Manchester United are believed to remain keen on Rose, but whether or not they pursue Tierney could obviously have an effect on Rose’s future.
Spurs have also been linked with Fulham sensation Ryan Sessegnon, although he has been playing in a more advanced role this term.
Both Tierney and Sessegnon are unproven in the Premier League, which could have a bearing on Tottenham’s decision to chase either one of them.