Goal reported on Sunday that both Premier League clubs are currently negotiating the transfer of the Chile star, whose contract expires at the end of the season.
City failed to reach an agreement with Arsenal over Alexis last summer but are hopeful of triggering a deal in January, with the Gunners hoping for a fee of around £35 million.
Widespread reports have since followed claiming the 29-year-old - who played under City boss Pep Guardiola at Barcelona - has an agreement with the league leaders.
However, Wenger says he has “nothing” new to report about Alexis, telling a press conference on Tuesday: “When solicitations happen you respond to it but at the moment it's very quiet.
“I have nothing to add to what I said before on that."
Goal understands Alexis is desperate for the move to go through and City are hopeful they could land him for around £25m.
Alexis has scored eight goals and registered four assists in all competitions for Arsenal so far this season.
The forward was part of the Barcelona side which won the 2011/12 Copa del Rey under Guardiola before the Catalan stepped down at the end of that season.