The Chilean forward has one more season on his current deal and looks set to stay after manager Arsene Wenger stood firm in the face of relentless transfer speculation this summer.
The club risk losing the 28-year-old for free at the end of his deal and need to have Sanchez at his very best in 2017/18.
Concerns were raised when he posted a message of social media shortly before pre-season training declaring himself ‘sick’ and, although he has since resumed work at Arsenal’s London Colney base, he did not feature in Sunday’s Community Shield win over Chelsea.
Keown does not expect commitment to be an issue, though.
“I don’t think Sanchez is the kind of player to shut up shop,” the former England defender told Press Association Sport at the FA and McDonald’s Community Awards.
“Wenger will be relying on the fact he’s someone who loves playing football and giving his all. They can work something out because he’s certainly made his mark at the club and been successful, so if he’s going to go he should do it in a dignified way.
“He signed a contract in good faith and – while he could probably move and earn a lot more money at another club – sometimes it’s about carrying on with dignity and respect and finishing the job. That’s what he should do at Arsenal.
“Wenger is probably hoping he can somehow win the Premier League and keep Sanchez, meet his needs from a trophy point of view and find some way to match his contract demands – but I don’t see that happening.”
Wenger has strengthened his squad since finishing fifth last term, adding Alexandre Lacazette up front and Sead Kolasinac at the back, but there has also been an intriguing backroom appointment.
Jens Lehmann, the club’s former goalkeeper, has returned as first-team coach and Keown, who briefly shared a dressing room with the German, believes he has plenty to offer the current generation.
“Jens is probably the only person I’ve met in football who is more intense than me,” he said.
“There’s a steeliness about him, a determination and a real professionalism. He’s a winner. When he first arrived he picked up the mentality of the dressing room so quickly, the way we did things at Arsenal.
“It doesn’t surprise me that Arsene has reached out to him, they’re not dissimilar in terms of outlook and Wenger may have seen something of himself in Jens.”