The Chile star, who, like reported Manchester United target Ozil, is out of contract at the end of the season, has been heavily linked with a January move to City after seeing a move break down at the end of the previous transfer window.
Although Pep Guardiola has insisted that he expects Alexis to stay at the Emirates Stadium, Goal understands the attacker is desperate to leave and is hoping to persuade the Premier League leaders to snap him up this month.
Alexis has been accused of dividing the Arsenal dressing room this season, but Wenger says they are hoping to persuade him to stay and maintains they have no fear that they will lose him or the Germany international.
"We have not been contacted by anyone," he told reporters on Tuesday. "This club has lost many big players and responded well.
“But you want to keep your best players. I want them to stay. Why should I be scared?"
Even if the stars do depart this summer, Wenger has no doubt that the club will be able to find adequate replacements for them.
"It will depend as well on the players out of contract in June. We have to take that and respond to it," he said.
“We have not lost them yet and [if we do], we will respond by bringing in players of top quality.
“We have not been contacted by anybody."
Arsenal are back in action on Wednesday when they host Premier League champions Chelsea at the Emirates.