The Scotland international is a summer target for Unai Emery’s side, but they face competition from Serie A side Napoli.
Sky Sports News reports that the Gunners submitted a bit worth around £25 million for the 22-year-old.
However, it was knocked back by the Scottish champions, who weren’t satisfied by the payment structure and want more cash up front.
Celtic are determined to resist interest in the left-back, who is currently recovering from a double hernia operation, until their valuation is met.
Tierney played 26 games in all competitions for the Bhoys last season as Neil Lennon's side claimed a historic treble-treble.
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