Spurs are currently stuck in a rut with recent defeats to Burnley and Chelsea meaning Mauricio Pochettino is under pressure going into Saturday’s showdown (12.30pm).
Meanwhile, over in Spain, and Bale’s time at Real Madrid continues to go from bad to worse.
The Wales international has fallen down Santiago Solari’s pecking order, starting the club’s last three matches on the bench.
Reports have even claimed that Bale no longer has the backing of the Los Blancos dressing room.
As a result of Bale’s struggles, many are tipping Tottenham to make him their marquee signing of the summer.
But Pires has mischievously urged Arsenal to pursue the forward instead.
“I think there’s a good chance Gareth Bale might be playing his last season at Real Madrid,” he told BWIN.
“He is having a very tough time on and off the pitch at the moment, and there are a lot of questions about how settled he is in the dressing room and how appreciated he is by the fans.
“You can see that Bale is an unhappy player at the moment.
“I think coming back to the Premier League is the most logical step for Gareth Bale.
“There’s an assumption that he would go back to Tottenham, but I would encourage Arsenal to open the door to the Emirates for him.
“I know Tottenham fans would not be happy, but Bale would be very welcome at Arsenal.
“I hope the club tries to see if it is an option this summer.”
Pires also believes Arsenal should pursue Crystal Palace youngster Aaron Wan-Bissaka.
“Arsenal should definitely be looking to sign Wan-Bissaka in the summer transfer window,” the former Invincible added.
“He’s exactly the type of player that would suit the attacking full-back role that Arsenal like to play and he would definitely improve the team next season.
“[Hector] Bellerín will have a long road to recovery and Arsenal won’t be wanting to rush him back in too quickly.
“There’s also the chance that his injury will be a recurring one so they need to have another full-back of the same high quality and I think Wan-Bissaka is that player.”