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 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 wages 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.
Read the full article on eurosport.co.uk: Arsenal won't break wage structure for Alexis Sanchez, says Arsene Wenger