The Gunners were hopeful that their improved bid would be accepted by Celtic, in what would have been a record Scottish transfer.
But according to the Sun, Arsenal’s tempting offer has been turned down due to the structure of the proposed deal.
Celtic are standing very firm against Arsenal in their pursuit of left-back Kieran Tierney
The Scottish giants are open to letting Tierney leave for the Premier League but they are holding out for £25m upfront.
Unai Emery’s side are expected to make a third offer for the Scotland international as they look to wrap up his signing as soon as possible before the new season.
Emery, who saw an opening £15m bid rejected, is eager to sign a new left-back to provide competition for Nacho Monreal and Sead Kolasinac.
Arsenal manager Unai Emery is eager to acquire the services of Tierney as quickly as possible