Celtic are reported to be interested in signing the Kilmarnock defender.
Tierney signed for the Gunners in a £25m deal, bringing an end to the transfer saga that has dragged on all summer.
It's now on the Hoops to put it all behind them and use their newfound resources to reinvest directly back into Neil Lennon's team.
There are a number of positions that need strengthened and left-back is now an obvious one.
Tierney's exit means there is a real lack of depth there, with Boli Bolingoli needing support and competition ahead of a long, difficult season.
Taylor has been a stand-out for Kilmarnock, emerging as one of the best young defenders in the division under Steve Clarke.
His former club boss was impressed enough with his progress to make him one of his first call ups as Scotland manager, with the 21-year-old starting against Belgium this summer.
As left-back options go Celtic could do far worse than bringing in a player who excels at Scottish Premiership level and has the potential to improve further.
Whether the club could sell the transfer to supporters is another story.
Would the majority accept a relatively cheap signing in place of selling their most valuable export ever?
Some fans are certainly keen, with this bunch taking to Twitter to share their thoughts on it all...
Greg Taylor would be a good signing don’t @ me— owen (@OwenR67) August 7, 2019
Greg Taylor from Killie looks the natural replacement for KT for me. 21 years old, Scottish, well established as top performer in the league and already capped for Scotland— Liam McLaughlan (@LiamMcLaughlan) August 8, 2019
I'd take Greg Taylor of Kilmarnock by the way hes impressed me everytime hes played— Sean Berry (@berrier7) August 8, 2019
100% agree. That’s who I would go for. Didn’t let himself down at all for Scotland against Belgium as well— ChristopherGillespie (@christopher1g89) August 7, 2019
@CelticFC Greg Taylor of @KilmarnockFC is placed highly on the list of replacements for Kieran #Tierney, Taylor had a terrific season under boss Steve Clarke last campaign & his age and ability suits Celtic down to a T. This could be just the LB that the club needs. #TransferTalk— EmCe (@SoccerzineUK) August 8, 2019
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