The Gunners had been touted as a possible destination for the highly-rated 20-year-old, who has attracted interest from a host of Premier League clubs.
It is understood that Zaha is close to securing a £12m transfer to Manchester United this month and could be loaned back to Palace for the rest of the season.
And Arsenal boss Wenger insisted that the north Londoners were “never” close to signing the winger.
“If Zaha goes to Man Utd, good luck to him,” Wenger told a press conference on Tuesday. “We were never in for him. Never.”
Zaha has netted five league goals in 26 appearances for Crystal Palace so far this season.
MORE: The latest football news