"Don't worry, I know what I will do in my future", Wenger told reporters.
The unceratinty comes as some fans paid to have a fly past protest during the game at The Hawthornes.
A plane flying a banner that read, "NO CONTRACT WENGER OUT" flew over West Brom Saturday, making it clear that some fans want to take the decision out of his hands.
"They were nowhere near the desire and the commitment needed to win a game in the Premier League", he said.
Arsenal manager Arsene Wenger follows the game, during the English Premier League soccer match between West Bromwich Albion and Arsenal, at The Hawthorns, in West Bromwich, England, Saturday March 18, 2017.
"I don't know about that", said Wenger.
Supporters renewed calls for him to step down during and after the defeat at West Brom, with some holding up "WENGER OUT" banners. "Financially, I mean. Of course, on the sporting front it would be a blow, but financially the Champions League does not have the impact any more that it had five or six years ago because of the influx of the television money (to the Premier League)". As long as I am at the club, whether that is for two more years, 10 more years or four more months, that will not be different.
"I made a decision to take him off and his ankle doesn't look good", Wenger said.
Arsenal's support is split over Wenger, who won seven trophies in his first nine seasons as manager but has won only two FA Cups in the 12 years since.
Wenger revealed Sanchez had been substituted with an ankle injury, which will be assessed before the club decide whether to withdraw him from the Chile squad. He should not have played in the second half but he insisted that he wanted to come out.
Barely two minutes after coming on for Rondon, Hal Robson-Kanu seized on a mistake from David Ospina to restore West Brom's lead 11 minutes after the break before Dawson added the Baggies third in the final quarter of the game.
Arsenal midfielder Alex Oxlade-Chamberlain apologised to the club's fans after the game, describing their performance as "not acceptable".