Sky Sports is reporting that the Scottish side have turned down the Gunners’ latest offer for the 22-year-old full-back.
According to the same story, Celtic are not happy at the way Arsenal have structured the deal and want more cash up front rather than in add-ons.
The same article says that the Scottish club are reluctant to sell their top asset unless the deal matches their valuation of the full-back.
It is claimed in the same story that Arsenal could be facing competition from Serie A side Napoli, who are said to retain an interest in the defender.
Tierney, who is under contract at Celtic until 2023, is currently sidelined after undergoing surgery on a hernia.
Arsenal have so far only signed Brazilian teenager Gabriel Martinelli this summer and it remains to be seen whether the Gunners will be able to get a deal over the line for Tierney.
The north London side finished in fifth place in the Premier League table and without a trophy last season after they lost the Europa League final 4-1 to Chelsea FC.
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