The Chile forward has a little over a year remaining on his current contract and his form this season has seen the likes of Paris St Germain, Chelsea and Manchester City linked with his signature.
Sanchez has also reached the six-man shortlist for the PFA Player of the Year award after scoring 22 goals and laying on 17 assists so far.
Arsenal are yet to officially open negotiations with Sanchez or the likes of Mesut Ozil and Alex Oxlade-Chamberlain, whose deals also expire in 2018, but the London Evening Standard reported on Thursday that a £300,000 (€354,000) a week offer for Sanchez had been tabled.
Such a move would smash Arsenal’s wage structure but, with Champions League qualification no longer a certainty following a run of seven defeats in 12 games, it may be essential to keep Sanchez out of the grasp of any potential suitors.
Despite that, Wenger is not ready to break the wage ceiling that has been put in place at the club.
“You have many different opinions there,” he said.
“Some people tell me ‘just give him what he wants’, but then you cannot respect anymore any wage structure and you put the club in trouble as well.
“That is why you have to make the decision in an objective way. Always the club has to be the priority.
“I understand as well that top players is a big priority but, at the end of the day, even for important players you can only pay as much as you can afford.
“We must accept that also modern life has changed a little bit and we always had a wage schedule that was respected, but players earn so much money now that the cases have become much more individual than global.”
Wenger refused to confirm speculation that a contract of such proportion had been prepared to keep Sanchez.
“First of all, I cannot confirm that we have offered that,” he said.
“Secondly, we will do as always. We have to consider our financial potential to sustain the wages for the whole squad.
“What is for sure is that what is paid per week today was 20 years ago per year. Will that continue to go up? I don’t know. I’m always tempted to say no but I was wrong on that front.”
Asked his thoughts about Sanchez being shortlisted for player of the year award, Wenger replied: “I’m very happy because it rewards a very strong season if you look at his numbers.
“His goalscoring record is good, his assists are good, and I believe that the combination of goalscoring and assists always shows the quality of a player.”
Earlier in the season it was claimed that both Sanchez and Ozil are seeking parity with the Premier League’s best-paid players before committing to the Gunners.
However, such figures are now skewed given how much money is on offer for top players if they move to the burgeoning Chinese Super League, but Wenger reckons the pull of the Premier League still tops the riches of the Far East.
“It certainly contributes to the imagination of the players,” he said of China inflating the figures on offer.
“I think every club and every player has to make decisions. Where are your priorities, where do you want to play?
“I think the first priority for top players is to play with the best players and in the best league. So after that it is not any more today where we have to make a choice, I go to China because you earn big money.
“You make big money in England as well. So you can combine the best combination of playing at the top and big money is in England at the moment. So China for me is not a debate.”
- Arsenal have acted fast to sign Schalke’s highly-rated left-back Sead Kolasinac on a free transfer.
Wenger has been quick to identify the Bosnian international as the successor to Nacho Monreal.
According to reports in Germany and Bosnia, Wenger has snapped up the defender on a free transfer after Kolasinac chose not to extend his contract.