Under pressure and out of contract at the end of the season, Wenger says he has made a decision on his future, but is yet to reveal it.
Arsenal have been forced to deny a reported approach for Borussia Dortmund boss Thomas Tuchel, but Smith thinks the club would be wise to sound out potential replacements.
Reacting to Arsenal's rebuttal over Tuchel, he named Juventus head coach Massimiliano Allegri and Monaco boss Leonardo Jardim as the calibre of candidate Arsenal should be pursuing.
"If Arsenal are not sounding out managers at this stage there is something badly wrong, they are not doing their job," Smith, who played for Arsenal between 1987 and 1995, said.
"If Wenger said tomorrow, 'Right, I'm leaving' then Arsenal would be left high and dry because they would have to scramble to see who might be out there and who might be available.
"They have got to sound people out. That would only be natural. Whether that is through a third party or whatever - that happens all the time.
"Allegri has been mentioned at Juventus and there is Jardim, the coach at Monaco, who has done really well.
"It is a plum job. I have said this before about Arsenal. They will be scrambling over each other to get into the hot seat. It is a fantastic job to take."
Smith added: "It is a beautiful stadium in London where a lot of the foreign managers want to come and a lot of the foreign players want to come. I don't think that advantage is being exploited enough at the moment.
"But as a board they have to be looking at who might be available if Wenger does walk away."
Arsenal lost 3-1 to West Brom on Saturday, a result that saw them slip to sixth in the Premier League when Manchester United defeated Middlesbrough the following day.