Mauricio Pochettino's side are known to be long-term admirers of the Scottish international's talents and did make and enquiry this summer, but like Everton and Bournemouth they decided against pursuing a deal after being quoted £25m.
However, Celtic have since been knocked out of the Champions League in the qualifying rounds after being edged out by AEK Athens, something which looks set to cost the club millions.
The aforementioned source claims that the 'Hoops' must now find and plug a £27m drop in income, with Tottenham looking to take advantage with a £10m bid for the 21-year-old.
Spurs are on the lookout for another option at left-back as Danny Rose's future remains up in the air and Tierney age and potential make him the perfect profile for a Pochettino signing.
It remains to be seen whether Celtic's financial needs are pressing enough for them to drop their asking price by more than half, whilst the Scottish outfit will no doubt see solace in the fact that Spurs were keen on a number of players this summer and instead became the first team to fail to make a transfer in the summer window since the introduction of the current system.