Celtic majority shareholder Dermot Desmond admitted he would let manager Brendan Rodgers speak to Arsenal if the Premier League club approached the Northern Irishman.
Wenger announced on Friday that he will step down at the end of the season.
The 68-year-old's position has come under intense scrutiny over the past 18 months due to repeated failings in the Premier League and Champions League.
Rodgers is among the favourites to succeed Wenger, and is on the verge of an unprecedented double treble with Celtic.
Asked whether Celtic would allow Rodgers to speak to Arsenal if they approached the coach, Bhoys chief Desmond told Sky Sports News: "Absolutely. I don't think you can put handcuffs on anybody if they want to go to a club as good as Arsenal.
"It will be Brendan's decision and Brendan's decision only."
Standard Sport understands that Wenger told his coaching staff on Friday morning before addressing the players in the first-team dressing room at Arsenal’s London Colney training base at 9.45am.
Wenger asked the club to delay making the announcement public until he had a chance to inform the squad. Official confirmation appeared on the Gunners’ website shortly before 10pm.
"After careful consideration and following discussions with the club, I feel it is the right time for me to step down at the end of the season," a statement released on the club's website read.
"I am grateful for having had the privilege to serve the club for so many memorable years."
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"After careful consideration and following discussions with the club, I feel it is the right time for me to step down at the end of the season," he said.
"I am grateful for having had the privilege to serve the club for so many memorable years.
"I managed the club with full commitment and integrity.
"I want to thank the staff, the players, the directors and the fans who make this club so special.
"I urge our fans to stand behind the team to finish on a high. To all the Arsenal lovers, take care of the values of the club. My love and support for ever."
