Tierney is part of an ongoing transfer saga, with Arsenal and Napoli the two interested parties.
The 22-year-old is a fan favourite at Parkhead and has close ties with the Scottish giants.
However, journalist Spiers, who writes for Scotland's edition of The Times, has revealed that Tierney's head has likely been turned.
"Those of us who have spent the past 10 days with Celtic became convinced that, if the circumstances were right, Tierney will want to leave," Spiers writes in The Times.
"Anything could happen; injury, breakdown in negotiation, Arsenal pulling out, but these seem unlikely. It looks to me he'll leave".
Celtic have been holding out for a fee of £25 million, but reports suggest Arsenal could seal a deal for closer to £22m.
The Bhoys have already secured a replacement for Tierney by signing Boli Bolingoli-Mbombo from Rapid Vienna.
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