Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Uzbek billionaire Alisher Usmanov, the club's second-largest shareholder, on Thursday reiterated in an interview with American broadcaster CNBC his desire to further invest in the Barclays Premier League club.
Usmanov - whose Red & White Holdings group are not represented on the board - also claimed Wenger did not have enough backing and blasted the decision to sell captain Robin van Persie to rivals Manchester United in a £24million deal last summer.
Wenger, though, feels the club's policy of self-sustainability will pay dividends in the long term.
Speaking ahead of Saturday's Barclays Premier League trip to Wigan, Wenger said: "I believe I have always had the support from the board, and am very grateful for that. We have worked over the years in respecting in what we did, which is to always work within our financial resources.
"Therefore we made decisions which from outside looked not based on purely footballing reasons, but it was based as well on financial reasons."
Arsenal announced new long-term deals for England midfielder Jack Wilshere and four other young players - Alex Oxlade-Chamberlain, Kieran Gibbs, Carl Jenkinson and Aaron Ramsey on Wednesday.
Wenger remains hopeful England winger Theo Walcott will follow suit and commit his future to Arsenal, with his contract set to expire at the end of the season.
The Gunners boss, however, insists just simply spending big in the January sales will not necessarily take Arsenal forward.
He added: "What is important is this team develops in the way we want to play.
"I have seen some interesting aspects on Monday night at Reading.
"Let's see how far this team can go.
"If we can add one or two exceptional players, we will do it.
"What we do not want to do is add players just because people put us under pressure to buy players.
"That is where we have to be strong enough. If we find a player who will give us something special, we will do it - but that in January will not be easy.
"We have money, and why should I not spend it if it is to find the right players?
"I believe as well the first and most important thing is to keep confidence in the players we have.
"If we are consistent, we can come back."
Usmanov, 59, has an estimated fortune of some £18billion and maintains his long-term ambition is to take a controlling interest in Arsenal, where American Stan Kroenke is the majority shareholder.
Speaking to CNBC from Moscow, Usmanov said: "I want to take this opportunity to just reaffirm that in order to help the team, we would be ready to buy more shares, to buy control, to buy all shares.
"We are ready to do all that we can in order to help the company, in order to consider any form of co-operation or ownership with the team.
"If I have a big stake in Arsenal of course I have my opinion what we must do, for example in the commercial side there are many questions over the effectiveness of the commercial side of Arsenal today, but we will see, we will wait and maybe when I wake up some day I have this Arsenal club."
Usmanov continued: "I always tell Mr Wenger he is one of the best coaches and football managers in the world, but I openly admit he has many, many difficulties to contend with.
"This decision (selling Van Persie) was a mistake. If I am one of Wenger's players I would want to stay for the finish, but he explained Robin wanted to go to win trophies."