"I can't tell you that at the moment", he said. "He is focused. Of course when you have treatment on a medical bench, it's not easy".
Sanchez's Arsenal future has been subject of intense speculation throughout the off-season with Bayern Munich and Paris Saint-Germain backing out of a chase for the Chilean, who reportedly still interests Manchester City.
The striker is expected to be sidelined for up to two weeks with a muscular injury and will miss the start of the new Premier League season.
Pressed by fellow panellist and BBC Match of the Day presenter Gary Lineker whether he genuinely did not know until the latter stage of the season whether he knew he would be staying or not, Wenger said: "No".
"He adds great value to the squad and I think as well he is a great lover of the club".
Now Sanchez is a hard choice - to sign the main contract of his life or go to another club who set themselves more ambitious goals.
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One of their 15 draws came last season but was at Turf Moor, which also witnessed 10 of their 11 league wins for the season. At the other end, Peter Crouch has six Premier League goals against the Toffees including one last season.
That is a bold move from the Gunners as it would make the former Barcelona star the highest paid player in the Premier League were he to sign.
That Wenger is not going into the new campaign with the fans still at his throat owes much to Arsenal's strong finish to last season.
"Plenty of uncertainties about players who didn't play against Chelsea - Ramsey, Ozil, Mertesacker".
Arsenal have signed two players so far this summer as they prepare to try and challenge for the Premier League title this season.
The Chile forward missed pre-season after being granted extra time off following the Confederations Cup and has been ruled out of Friday's game due to an abdominal strain.
"I have players coming back who have not played, like [Shkodran] Mustafi".