A survey has revealed 78 per cent of members want the long-serving Frenchman out at the end of his current contract in the summer, and have urged the board to withdraw the offer of a new two-year deal.
Hopes of securing a Champions League place for a 20th consecutive season have hit the buffers with a run four defeats in their last five Premier League games, prompting Gunners fans to turn on Wenger.
But Guardiola, who takes his Manchester City team to the Emirates in the Premier League on Sunday, believes he can win the fans over just by getting back to winning ways.
“When he goes back to winning, the fans will be happy again. I promise you, 100 per cent,” said the City boss.
“The Premier League is not easy to win but I’m pretty sure the fans respect a lot what Arsene Wenger has done and is doing.
“People should understand how difficult football is today. All the teams are more prepared.”
Wenger, in his 21st year with Arsenal, is the longest serving manager in English professional football. And Guardiola, who lauded the 67-year-old as the “commander in chief” the last time the teams met in December, stressed that longevity is testament to his quality.
“I think a manger like Arsene, who has had a lot of years in one team, is so important,” said the Spaniard.
“You cannot stay, I don’t know how many years Arsene has been in charge of Arsenal, without ability.
“To have here a friend of mine [on the City coaching staff], Mikel Arteta, who was with him for a lot of years, only has good words about Arsene. I believe more in that.
“Managers lose games. He’s there a long time because he’s good. If not, it cannot happen.”
Of Wenger’s future, Guardiola added: “When the bosses decide, or Arsene decides, to stay and keep going he believes it is the best solution and the best for Arsenal.
“I’m not here to judge what they have to do and what is going to happen. The players judge what they see every day in the training sessions and how we are. Some of them are happy, some of them are unhappy especially the players who don’t play.
“But for the fans it depends on results not something else.”
Guardiola, though, will be hoping to extend Arsenal’s miserable run to cement City’s position in the top four, but is wary of a wounded animal mentality from the Gunners.
“When you lose a lot of games it is a dangerous moment. I would prefer to take Arsenal after a lot of wins,” he said.
“Everybody knows them - good quality in the middle, good quality in the sides with Alexis going inside, runs in behind with Walcott, Chamberlain. Good quality. Arsenal is a top team.
“I know how difficult it will be, but of course we have a good chance to make a step forward.”
Guardiola remains without long-term casualties Ilkay Gundogan and Gabriel Jesus but is hopeful of having Kevin De Bruyne and Pablo Zabaleta available to face Arsenal.
“They are not top, top perfect but yes,” he said, adding that he is optimistic that Jesus can return to the squad before the end of the season.
“Hopefully he can help us and come back for us in the pre-season,” he said.