Former Gunners striker Ian Wright said he believed the 67-year-old Wenger's time with the Premier League team was "coming to the end," based on remarks which Wright said the manager had made on Thursday evening.
Having watched his side respond to back-to-back league defeats with a 2-0 win over Hull on Saturday, Wenger said the media pundit had misinterpreted him and insisted they had no private conversation.
"I didn't give any indication about my future," Wenger said. "It was a question and answer with members of the club, there were many people there. We had a little dinner before but we were not the two of us, we were four or five."
"I appreciate that you want me to rest, but I'm not ready for that."
With no Premier League title since the 2003-04 season, sections of the club's fan base have grown frustrated with Wenger.
Wright, who played under Wenger at Arsenal for two seasons following the Frenchman's arrival at the club in 1996, had shared his views with BBC Radio Five Live on Friday.
"I was with the boss last night and if I'm going to be totally honest I get the impression that that's it," Wright said. "I genuinely believe - I was with him for a few hours last night and he didn't exactly tell me that he's leaving at the end of the season - but you get the impression looking at him that that's it."
"I think that's it. He actually mentioned when he was talking last night that he's coming to the end. And I've never heard him say that before."