Zaha has emerged as one of the most exciting prospects in the English game over the last few years.
Manchester United admit they are pursuing the 20-year-old, with some reports suggesting that the Premier League leaders are close to agreeing a £15 million deal for the England international.
Arsenal were also reported to be interested in Zaha, but the Gunners boss insisted that was never the case.
"We were never in for Zaha," Wenger told a press conference. "I don't know if he will go to Man United. If he goes to Man United, good luck to him."
Wenger, who lost Robin van Persie to United last summer, knows his side are incapable of catching the Red Devils, who top the table with 56 points, some 22 ahead of the north London club, who used to be their main challengers for the title.
Indeed Arsenal are seven points off fourth place, although they have a chance to shorten that gap if they beat West Ham on Wednesday.
Wenger, who has guided his team to 15 consecutive top-four finishes, admits he is concerned at his team's plight.
"What is worrying is just that we do not win the big games," said Wenger, who watched his team lose 2-1 at Chelsea on Sunday.
"At the moment we do not get the results we want.
"The difference in points mathematically is not dramatic, but the consistency of our performances within games is what is worrying."