Wenger, who has been Arsenal's manager since 1996, has come under pressure from fans for the first time after a sixth successive season without a trophy ended so disappointingly with just three wins out of their last 15 matches.
Fabregas has again been linked with a move back to his boyhood club Barcelona, while French international forward Nasri could be on his way too, with Manchester United, Manchester City and Chelsea all circling.
Arsenal leave for their pre-season tour of the Far East on Sunday when they fly to Malaysia with Nasri on the plane but Fabregas will remain behind with a hamstring problem.
Wenger, returning from his summer break, had this message for Arsenal fans when he spoke to the club's website.
"I can promise you that we will work very hard and we have had some long nights to achieve what we want to achieve," he said, adding that he would not buy just for the sake of it.
"If there was an obvious choice, people would have already made their decisions," he said.
"Everybody needs the same players for the same positions. We are at the top level and therefore need exceptional quality to strengthen our side.
"I can understand that people say 'you have money, just go out and buy', but it's not only that, we want to find the quality we need."
Regarding his club captain Fabregas and Nasri, Wenger said: "Our position is always the same - we want to keep Cesc and I will fight as hard as I can to keep him. Samir Nasri is exactly the same. We will do everything we can to keep him."
Arsenal were expected to announce that Lille striker Gervinho is joining on a four-year deal after completing his medical.
Other targets include Bolton centre-back Gary Cahill, Valencia's Spanish Under-21 midfielder Juan Mata, Blackburn Rovers defender Chris Samba and Real Madrid striker Karim Benzema.
Wenger does have money to spend. Arsenal are in a healthy financial situation and he added some 7.0 million pounds to his transfer funds this week when defender Gael Clichy left for Manchester City.
Their only definite signing so far is promising 19-year-old defender Carl Jenkinson from League One Charlton Athletic for one million pounds.
Wenger added: "I have said many times that we have been very close, despite the disappointment we had at the end of the season, we were very close again to winning things.
"I hope that provokes a response from my players to think we we were so close. We want to come back and achieve it.
"My responsibility is first of all, not to lose players and then to add and make us stronger. Lets hope we can bring in one or two more additions of top quality."
Arsenal's first tour match is against a Malaysia XI on Wednesday, followed by a fixture against Hangzhou Greentown on July 16.
They start their Premier League campaign away at Newcastle United on August 13.
