The Chile striker can leave for free this summer when his contract expires and he has been linked with a move to league leaders Manchester City, who failed in their bid to sign him on deadline day.
When asked about the 29-year-old’s future, the Frenchman said: “Nobody knows what will happen. It’s difficult to speculate.
“We are focused on short term, that means the next game with the players committed and ready to fight. It’s not a guarantee of how long you stay somewhere.
“They are questioned, always, when people don’t have long contracts. The best way to show they are committed is to give that kind of performance.”
His comments come only a month after he said that both Sanchez and German midfielder Mesut Ozil, whose current deal also expires in the summer, want to stay at the Emirates Stadium.
On Thursday, Sanchez struck twice in four minutes after Andros Townsend had cancelled out Shkodran Mustafi’s first-half opener.
The forward squeezed a clinical strike in at the near post to make it 2-1 before bringing Jack Wilshere’s superb ball from his own half under control and flicking into the net.
James Tomkins headed in late on but Sanchez’s double was enough to secure a win that keeps sixth-placed Arsenal level on points with Tottenham, who are fifth, and one point behind fourth-placed Liverpool.
|Most games managed in the Premier League|
|Manager||Games||Wins||Draws||Losses||Goals for||Goals against||Win %|
|Sir Alex Ferguson||810||528||168||114||1,627||703||65.2|
The best and worst of Arsenal on show
After three draws and just one win from their four previous Premier League outings, this was arguably an important game for the Gunners in their bid to remain in the hunt for a top-four finish, especially after wins for rivals Tottenham, Liverpool and Chelsea in midweek.
They started the day with six points fewer than they had at the same stage last season – and Wenger’s side ultimately finished outside the Champions League places – so a positive result and performance was needed to help ease any Arsenal fans’ concerns their campaign was in danger of fizzling out.
For large periods, the performance was certainly there. The visitors often produced some of their best attacking play of the season, particularly in the first half when Palace could not cope with short, intricate passing that time and again opened up the defence.
But their inability to finish off the many opportunities they created meant their opponents always had a chance to get back into the game. That proved the case early in the second half when Zaha’s cross caught Arsenal’s defence asleep and Townsend struck.