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The 28-year-old forward, who is a reported target for Manchester City and Paris St-Germain, is entering the final year of his deal at Emirates Stadium.
He was granted an extended summer break after playing for Chile in the Confederations Cup but only returned to training on Tuesday after illness.
"The only thing I can tell you is he is focused," said Wenger.
"My decision is clear - he will stay and he will respect that."
The Frenchman, 67, said he would no longer speak publicly about speculation over Sanchez's future, adding: "It is not information anymore, it is suicide.
"He will be here for this season and if we manage to do it for more seasons, we will do it as well."
Wenger also confirmed that Spanish striker Lucas Perez will be allowed to leave the Gunners, with former club Deportivo La Coruna reportedly having made a bid to re-sign the 28-year-old.
"We have a congestion of strikers - I don't want to lose him but too much competition is not competition any more," said Wenger.
"If he finds a satisfying solution, at least for a short time, we will do it."
Perez joined Arsenal for £17.1m last summer after two seasons at Spanish side Deportivo, but has not played since March.
Arsenal signed Alexandre Lacazette for a club record £46.5m fee this summer, with the 26-year-old France striker given Perez's number nine shirt.
Wenger added there was "nothing to announce" about other players entering the final year of contracts, including midfielder Alex Oxlade-Chamberlain, 23, and 27-year-old left-back Kieran Gibbs.
FA Cup holders Arsenal face Premier League champions Chelsea in the Community Shield final at Wembley Stadium on Sunday, with kick-off at 14:00 BST.
Alexis Sanchez will stay at Arsenal for this season and will "respect" that decision, says manager Arsene Wenger.