Barcelona had initially seen a ?27million offer rebuffed earlier inthe summer, as Arsenal remained steadfast in their demands over a ?40million fee for their captain.
Get me out of here: Cesc Fabregas is closing in on his dream return to Barcelona
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 Barclays 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.
Au revoir: Nasri is set to depart Arsenal for Manchester City
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.'
Were Fabregas - who missed the Asia tour and all of pre-season because, officially at least, he was troubled by a hamstring problem - to feature in next week's first leg of Arsenal's Champions League play-off against Udinese, the midfielder would be ineligible for any other side later in the competition, suggesting the deal will be pushed through before then.
Fabregas joined Arsenal as a raw youngster for nothing from Barcelona in 2003, and has made more than 300 appearances, scoring 57 goals, but the World Cup winner has yet to taste club success.
The sale of two key men on the eve of the new campaign is hardly the ideal preparation for another assault on ending Arsenal's six-year trophy drought.
Denmark striker Nicklas Bendtner, linked with Stoke, has yet to find a new club, while utility man Emmanuel Eboue is expected to sign for Galatasaray.
On his way: Spanish press convinced Fabregas will join Barcelona
However, Wenger - who has signed forwards Gervinho and Alex Chamberlain this summer - is expected to move quickly for replacements.
Valencia midfielder Juan Mata is a long-time target, while Costa Rican forward Joel Campbell is said to be close to a ?1million move to the Emirates Stadium.
Defensive reinforcements are top of the agenda, with a ?6million move for Birmingham's centre-half Scott Dann said to be imminent after Arsenal failed to complete a deal for Everton's Phil Jagielka or Gary Cahill from Bolton.
Former Gunners full-back Lee Dixon believes Arsenal are best off without players who no longer want to commit to the cause.
'You're better off getting ?60m for two players who don't want to stay and spending the money wisely,' Dixon - who the Double twice under Wenger - told BBC Sport.
'There is no doubt they are top quality players and they will be missed, but it is important that supporters and everyone at the club remembers that the cannon on the chest is more important than anybody.'
Arsenal have several fitness concerns ahead of the trip to St James' Park, where they blew a 4-0 half-time lead in February.
England duo Theo Walcott and Jack Wilshere are already doubts because of ankle injuries, along with striker Robin van Persie, who is carrying a similar problem. Wales skipper Aaron Ramsey (calf) came off against Australia as a precaution.
Au revoir, Cesc! Nasri set to beat Fabregas to Arsenal exit as ?22m City switch loomsFabregas: I will pay to leave Arsenal! Captain offers to give up ?4m in bonuses to force Barca moveCLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAME