According to The Sunday Business Post, the London club is looking to test Celtic's resolve by meeting their valuation with a bid of around £20m plus £5m in add-ons.
• READ MORE: Stephen Halliday: Celtic’s Kieran Tierney must let his head rule his heartThis latest approach has come after The Gunners had an initial bid of £15million thrown out by the Scottish champions with it being far below their valuation of the star which was reported to be £25m.
Unai Emery then followed up a second bid of around £18m, which was once again knocked back by Celtic and described as derisory by former Celtic and Arsenal star John Hartson.
It now seems that the Arsenal boss is ready to take the plunge and try to meet Celtic's valuation for the vastly experienced player.
However, boss Neil Lennon has previously stated that Tierney is on a long-term contract, and that the club "don’t want to sell him".