The Wales international continues to see his future called into question after enduring another injury-hit campaign which has seen further questions asked of his value and standing within the Blancos squad.
A return to the Premier League has been mooted for some time – with the likes of Manchester United and Chelsea said to be keen – and 2019 could be the year in which a deal is done.
Spurs would undoubtedly be interested were a man who starred for them prior to making a record-breaking switch to Spain become available, but Pires has urged the 29-year-old forward to consider a move to the other side of north London.
“I think there’s a good chance Gareth Bale might be playing his last season at Real Madrid,” a member of Arsenal’s ‘Invincibles’ squad 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.”
While seeing Bale as a good fit for Arsenal, Pires is not convinced that any effort should be made to bring Alexis Sanchez back to the club from an unhappy spell at Manchester United.
He said of the Chile international: “It would be very strange to see Arsenal sign Sanchez back in the summer. I don’t see how it makes sense for either Sanchez or Arsenal after how it ended. There’s no chance Sanchez will return to Arsenal.
“Sanchez isn’t playing his best football and he is on a lot of money at Manchester United which Arsenal are not willing to pay.
“Sanchez won’t want to come running back to Arsenal with his tail between his legs after having a rough time elsewhere. He will have to hope he returns to form with a fresh chance under [Ole Gunnar] Solskjaer at Manchester United.”
There is another player that Pires thinks the Gunners should be targeting, though, with Crystal Palace defender Aaron Wan-Bissaka generating plenty of interest from Premier League heavyweights.
Pires said of the 21-year-old right-back: “Arsenal should definitely be looking to sign Wan-Bissaka in the summer transfer window.
“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] Bellerin 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.”