Sanchez is free to open discussions with foreign clubs from Monday over a free summer transfer, having allowed his existing terms to expire.
Manchester City are the favourites to swoop for the Chile international at the end of the season, with Arsenal understood to be reluctant to offload midway through the campaign for a fee in excess of £20m.
As talk regarding Sanchez's future continues to rumble on, Wenger has suggested that he no longer cares where his star man ends up next.
"I don't know what is going on in his head and whether he is with us short term or long term. I am not a psychologist," he told reporters.
"From Monday he is free to go where he wants if it's a foreign club - but that's not my problem. My problem is just about trying to win the game at West Brom."
Sanchez, also linked with a move to Paris Saint-Germain and Real Madrid in the past, is expected to start Arsenal's final game of 2017 against West Bromwich Albion on Sunday afternoon.