Barcelona had initially seen a ?27million offer rebuffed earlier in the summer, as Arsenal remained steadfast in their demands over a ?40million fee for their captain.
However, with the European champions not willing to significantly up their cash bid, and Wenger admitting the player was unsettled, it now appears as if Arsenal will have to allow the deal to go through for less than they had wanted.
Reports have suggested a deal - understood to include a down payment of 30million euros (?27million), with an additional 6million euros (?5.2million) in performance-based add-ons - will be pushed through ahead of this weekend's Premier League opener at Newcastle.
Wenger confirmed to Arsenal Player: "That is completely the truth. We hope it will be sorted out very quickly one way or the other. We will know very quickly."
Nasri, meanwhile, has yet to pen a new deal, and so could leave for nothing next summer.
Manchester City are reported to be ready to bid up to ?25million for the France midfielder.
Wenger said: "The Nasri situation is stable. Again it is very difficult to speak about possible transfers, but we are in a situation where we have to make decisions one way or the other.
"Ideally you want it to be sorted out before the season starts."
Source: Team Talk
Source: Team Talk