However, that could all change on Tuesday when Sanchez finally returns - just five days before Arsenal face Chelsea in the Community Shield - with The Mirror reporting that he is considering handing in a transfer request to try and force through a move to Manchester City.
Sanchez's illness will not change Arsenal's stance.
Alexandre Lacazette gave Arsenal an injury scare as the club's record signing limped off after scoring his first home goal in Sunday's 2-1 Emirates Cup defeat against Sevilla.
Speaking at his post-match news conference at The Emirates on Saturday evening, Wenger said: "I think he has gone, in pre-season, from strength to strength".
Lucas Perez's future at Arsenal could soon become clearer after his agent flew into London and confirmed a bid had been tabled by Deportivo La Coruna.
"He has flu, yes", Wenger told reporters, as quoted by Arsenal's official website.
GREG BAKER GettyImages
Arsenal could yet attempt to reach some sort of compromise with Sanchez that includes the offer of a short-term one-year contract on £300,000-a-week - more than double his current £160,000 salary, with a promise to renew talks again at the end of the season.
City keeper Claudio Bravo, who plays with Sanchez for Chile, has now said: "If he decides to go, we'll wait for him with open arms at City". "Your job is to be suspicious".
"It's not the same".
Probed on whether Sanchez had personally told him whether or not he wanted to stay, Wenger added: "I can not reveal to you what he says to me always". I'm a fan and get excited when great players are taken on.
Will the Gunners have signed Thomas Lemar from Monaco by the time that game comes around? We come out [publicly] once the player is done or not done. "But at the moment there is nothing special to say in this case".
Managers are now pressing ahead with their plans for the summer transfer window so we'll bring you all the latest news and gossip from around the globe.
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