They will, though, need to do some groundwork as currently the £34million the Spanish title winners want for his services is too much for the Gunners.
But they may find some hope in a transfer deal they did long ago.
There's a feeling that Real Madrid can sign any player they want. That's not always the case when Arsene Wenger has something to say about it though.
Former Arsenal defender Lauren had seven incredible years in north London, winning two Premier League titles and three FA Cups.
It could have been a whole lot different for the Cameroonian, however, as Real Madrid got in first to sign the then-Mallorca full-back.
"My representative came to Madrid, met Juan Onieva [the vice-president] and they didn't reach an agreement because the economic conditions that Madrid offered didn't convince us," Lauren told the Daily Mail.
Lauren added how he and his agent got on a flight to London having had contact with Arsenal before. The reception couldn't have been more different.
"When we arrived we went straight to David Dein's house," he added. "It was David Dein, his daughter who spoke Spanish, Arsene Wenger, me, my representative, and a translator who we had brought with us because my English was non-existent.
"What really struck me was that I had always negotiated in an office with everyone very serious, wearing suits and ties. This was totally different. David Dein opens his home to you. His personality was spectacular, the treatment man to man was fantastic and I left there totally convinced."
Lauren signed shortly after, a great coup for the Gunners considering he grew up supporting Real Madrid.
Dein's pitch was clearly impressive but Lauren gives huge credit to Wenger for his contribution too.
"And Wenger, with that human warmth he has, that approachable character of his," Lauren added.
"During negotiations he didn't speak too much; he listens to you, watches you, he's seeing if you have the personality to be able to take on this challenge.
"At Madrid it was like you had to do what they said: this is the way it is, full stop. My dad is a Madrid fan, I was always a Sevilla fan and then Madrid as well, but when another club comes along with another attitude however much you might have liked Madrid, you go to the place where they treat you best and where they offer you the best terms.
"The way that Dein and Wenger acted struck us. It wasn't 'come to the club', it was 'come to my house. Come to be with my family, in my home. Come to join us.'"
As mentioned, Lauren had a great career at Arsenal and was part of their Invincibles squad that romped to what's still the club's most recent Premier League title.
It would be perfectly natural to wonder what life would have been like at the Bernabeu but Lauren insists he'd always pick Arsenal if greeted with that situation again.
"If I was born again I would sign with Arsenal ten more times because I played with top players, with a top manager, at a top institution with top human beings all around," Lauren told Goal.
"Arsenal is my family and it will always be my family because it's the place I grew up as a person in so many ways.
"It's not only about the trophies, it's not about money. It's more than that.
"Arsenal give you everything necessary to make you feel like you are in a family and I really feel that Arsenal is my family.
"It was the perfect moment for me and so many players would feel the same way.
"I remember once we were celebrating a trophy in the dressing room and we were all flying. Dennis Bergkamp said 'enjoy these moments lads because you never know if this is going to happen again'.
"So that's why I say I have no regrets and if I had to sign with Arsenal again, I would sign every single year for the rest of my life. If I had to do it again, I would sign for Arsenal rather than Real Madrid."
Download talkSPORT Edge NOW!
Whether it's goals as they go in or the latest from your club, stay up to date with everything going on in football with breaking news, live scores and in-app betting.
Download talkSPORT Edge in the App Store here.