The Gunners broke their club record transfer fee when they forked out £42.5 million to bring the Germany international to the Premier League from Madrid on deadline day in summer 2013.
However, Law explained that the deal might have never gone ahead if it wasn’t for negotiations that were taking place across town.
“Real Madrid, for all of their firepower, really stretched themselves when they bought Bale,” he told Goal.
“They paid an extraordinary amount of money for him and they gave him an extraordinary contract, what that meant was they needed to sell somebody. So it’s the Bale story that leads us to Ozil.
“We got signals from Madrid that they had players for sale, so I flew out to meet with Jose Angel Sanchez, the general manager of Madrid, and he said that the club would consider selling Karim Benzema or Angel Di Maria - and he gave me a number.
“So I called Ivan (Gazidis) and Arsene (Wenger). We were all very cautious and sceptical, but the one thing we knew based on that meeting was they had to sell someone.”
Law joined Arsenal in 2009 to work alongside Wenger and chief executive Gazidis on transfers and player contracts.
He explained that the Gunners hierarchy learned Madrid manager Carlo Ancelotti was willing to let Ozil go following another meeting with Sanchez, after the Italian vetoed the sales of Di Maria and Benzema.
However, with just 48 hours to go before the window shut, Spurs chairman Daniel Levy still hadn’t signed off on Bale’s sale.
With a north London derby coming up a day before the transfer deadline, Arsenal knew they couldn’t afford to alert Levy of their intentions.
“We had finalised a deal with Madrid,” said Law. “Ivan was there and I was now in Munich with Ozil - and this was literally the morning of the Tottenham match when Ivan calls me.
“He said that he couldn’t get back to London for the match because he was finishing up the agreement and that one of us needed to be in the directors' box or else Daniel Levy was going to get very nervous.
“Jose Angel had told Ivan that Levy had called him and said the one last condition of the Bale deal was Madrid couldn’t sell any players to Arsenal.
“Ivan’s response was that Levy was bluffing because he’d already spent the Bale money. But he still said to me that we couldn’t take a chance and asked if I could get from Munich to London to be in the directors' box because Tottenham were starting to think something was going down.
“So, I got a flight at 11am, changed on the way and when I walked into the directors' box I saw Franco Baldini and Levy. They asked what I was doing. I said it was the derby, I wasn’t going to miss it.”
After the match, which Arsenal won 1-0, one further complication arose when Law encountered Lukas Podolski at the Munich clinic where Ozil was set to complete his top-secret medical.
“That minute I called Arsene and said, 'This news is going to be out because Lukas can’t keep his mouth shut on a good day',” he said.
“The chairman then got news that Manchester United were going to try to cut across the deal. So Ivan called me and asked me to man-mark Ozil’s father and business advisor in Munich.
“I had to sit from 10am to 10pm in the bar at the Four Seasons taking calls from the contract team with questions about this clause and that clause. They eventually drafted everything and sent it over for Ozil to sign.”
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