Reports have suggested Arsenal have agreed to lower their demands for Fabregas and that he could finally make his return to Barcelona by the weekend, and Wenger has now confirmed that a decision will be taken in the imminent future.
"That is completely the truth," he told the club's official website on Thursday afternoon. "We hope it will be sorted out very quickly one way or the other. We'll know very quickly."
Reports in the French media had also said that Nasri was likely to be a Manchester City player before the season kicks off on Saturday and 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."
Asked whether either could already be considered a done deal, he replied: "No."
Former Arsenal defender Lee Dixon believes Wenger should take the money with both players unsettled.
"You're better off getting £60 million for two players who don't want to stay and spending the money wisely,'' he 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."