The Gunners were knocked by Celtic with an initial offer of £15m for the left-back.
Now they have returned with an increased bid, but The Times says that amount still does reach what Bhoys chief Peter Lowell is looking for.
The report claims the Scottish giants want at least £25m for the Scotland international.
Lowell knows that with other interest from Everton, Napoli and Leicester City, the reigning Scottish champions should get their desired fee.
The north London club are hoping to spend as little as their £45m transfer budget as possible.