With his contract at Bayern Munich ending in the summer and an announcement on his intentions expected next week, Guardiola has been linked with a move to the Barclays Premier League.
In varying reports, the Catalan is being lined up by the likes of Manchester United, Chelsea and City, should he opt not to extend his stay in Germany.
Pellegrini has already dealt with his position being threatened in the past and takes his side to the Emirates Stadium on Monday night looking to beat Arsenal in a match that could potentially see the victors topping the table at Christmas.
Wenger acknowledges such rumours can be unsettling, but feels his Chilean rival can deal with such talk.
Asked if links to Guardiola could be destabilising to Pellegrini's ambitions, Wenger replied: "It can be, but Pellegrini is experienced enough to deal with it.
"Maybe if it was a very young beginner, it could be destabilising, but I don't think that at his level it will affect him.
"I don't know if that (the speculation) is down to City - that's down to media speculation and I don't know where that comes from.
"It's very difficult to master nowadays, to have this kind of speculation
If you look at Real Madrid, there is always speculation
It looks like it's part of our job now."
Wenger dismissed any suggestion his side will take advantage of any issues that may arise over the uncertainty of Pellegrini's situation and wants Arsenal to think only of themselves on Monday.
"I believe that what will be an advantage to us is to focus on our performance and not hope for any weakness from City," he said.
"We go into a top-level game where all the rest will be forgotten and everybody else will just focus on the performance on the day.
"The number of goals scored and goals conceded, the number of passes made, percentage of possession, is all very close
If you look at all the numbers (Arsenal and City are very close)."
While Monday night's game will be about two teams with title aspirations, champions Chelsea languish just one point above the relegation zone.
After giving his support to Pellegrini, Wenger passed on the opportunity to give his backing to beleaguered Blues boss Jose Mourinho - with whom he has a chequered history.
Asked if Chelsea are in a relegation battle, the Frenchman said: "No, (because of) the quality of their team.
"If you ask me objectively, will Chelsea go down? I will say 'no chance'
They are going through a difficult spell but they are not in a relegation battle."
Wenger was then more evasive when questioned on the prospect of Mourinho being sacked.
"I do not want to assess any other things about Chelsea," he said
"It's not my problem - my problem is the game on Monday night."
He ended the discussion when asked if he had as much sympathy for Mourinho's plight as he would for other managers by saying: "I just gave you a good answer."
City will go into Monday's game buoyed by Sergio Aguero's return to fitness - but Arsenal are not giving up hope on their own talismanic frontman being fit for the clash.
Alexis Sanchez picked up a hamstring injury in the recent draw at Norwich but is also back in training, with Wenger revealing the Chile forward could be involved.
"Maybe there is a slight chance for Alexis to be in the squad again, but it is too early to be sure about it," he said.
"He is running but not participating in full training."
While the former Barcelona man will be raring to go, Wenger admits he cannot always believe a player who declares himself fit.
"Not all of them," he replied when asked if he trusts all the players who say they are fit to play.
"It is not trust in a negative way when I say all of them
Some of them are so keen to forget that they have pain somewhere that they say they are all right when they are not.
"You know the players and their psychological profile, you take that into account then you get scientific advice and you trust your gut as well and then you make a decision.
"I believe that is normal that he (Sanchez) wants to play
You want him to be keen to play
He respects all the decisions I make and that is what I want from him."
Source : PA