Arsène Wenger has said he is confident that Cesc Fábregas will remain an Arsenal player for "many years" to come, as the club's chief executive told shareholders that football's shifting economic sands and new European regulations would play in their favour.

Speaking at the club's annual general meeting, Wenger said Fábregas, the subject of intense interest and a £35m bid from his boyhood club Barcelona in the summer, stayed because he "loves Arsenal deeply". The manager said: "You also have to remember that Barcelona has an attraction, because he grew up there, but I believe he wants to win with this club. For how long? You never know but hopefully for many years."

"It is about our potential to win also, how well he can do. I am not pessimistic about him and I am confident we will keep him for a few more years."

Wenger, aware of the pressure to win the club's first trophy since 2005, faced questions from shareholders about his failure to buy a goalkeeper this summer and the side's defensive frailties. He said there was money available to add to the team in January but called on fans to trust him and get behind the team before Sunday's match at Manchester City.

"I see a real opportunity to have great achievements this season – we have the spirit, talent, hunger and desire," he said. "I do not say there are no weaknesses but we work very hard."

Wenger, who has been accused of undervaluing the domestic cups, said: "We will go for every single competition this season with every resource we have and we will give absolutely everything."

Wenger sidestepped a question from the floor about whether he would be interested in signing Wayne Rooney, saying the subject was "too sensitive". But he said the Manchester United striker's attempt to force the situation was a further example of the "inflationary" effect of the current system and the power of players since the Bosman ruling.

"It shows you how fragile the position of any club is at the moment, considering the length of contracts of players," he said. "When the players reach two years before the end of the contract, if you want to keep the value of it, you have to extend it or he will go for nothing in the end. The system is inflationary."

Wenger, who turns 62 tomorrow and recently signed a contract tying him to the club until 2014, vowed to continue in charge of the "club of my heart and my life" as long as he was physically able.

Ivan Gazidis, the club's chief executive, said recent results, which revealed pre-tax profits of £56m and showed the club no longer carried any debt attached to its property deals, proved its self-sustaining business model was working and left it well-placed to prosper under Uefa's financial fair-play regulations that are due to be introduced in 2012-13.

Peter Hill-Wood, the chairman, said that a "world-class" new commercial management team would be responsible for ensuring that the one-off cash injection from the property sales was replaced by new revenue streams.

Gazidis also made reference to the fact that Arsenal's major shareholders did not take a dividend, meaning "everything we earn [goes] back into the club", drawing an unspoken comparison to the situation at Liverpool under their former owners and Manchester United under the Glazers.

"Our club has built everything it has and everything it represents without relying on outside investment for success," Gazidis said, this time bringing to mind the benefactors at Manchester City and Chelsea.

"This is a challenging path to tread," he told the AGM, "but we have earned our independence. We do not have to rely on anybody but ourselves for future success. However, we have to keep moving forwards – standing still is not and never has been an option."

Members of the Arsenal Supporters' Trust fanshare scheme, which the sports minister, Hugh Robertson, believes could be a model for supporter representation at other clubs, were also present at the meeting, alongside Stan Kroenke, the club's largest shareholder.