West Brom stunned Arsenal with a 3-1 win on Saturday night (AEDT), with Wenger's men subsequently dropping to sixth in the Premier League after Manchester United's win at Middlesbrough.
The under-pressure Frenchman is out of contract at the end of the season and has made his decision on whether to stay at Emirates Stadium, but is yet to reveal it.
Pulis said before the match that he thought Wenger would want to carry on for another six years and a post-match chat with the Frenchman has not changed that opinion.
"I'll be surprised if he goes," Pulis told The Sun.
Pressed on why he thought that, the West Brom boss said: "Because he told me."
Pulis again offered Wenger his backing after a match that saw two planes fly over the Hawthorns, one with a message of support for the 67-year-old and another criticising him.
"I think he is the greatest manager Arsenal have ever had. They could finish in the top four and win an FA Cup – that is not too bad is it?," Pulis said.
"I don't think respect counts now. People live for today. If you are asking me what Arsenal should or shouldn't do I'm the wrong person."