Wenger's future had been questioned in the wake of defeats against Watford and Chelsea that effectively killed off their Premier League title hopes.
Wenger's side returned to winning ways as Alexis Sanchez's double secured a 2-0 home victory over Hull on Saturday.
But after the game the Frenchman was quizzed on his future, with his current contract expiring at the end of the season and a minority of fans turning on the manager for recent results.
"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 told BBC Radio 5 live.
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"He actually mentioned when we were talking that he's coming to the end. I've never heard him say that."
Yet Wenger countered by saying any tiredness stems from his commitment to the job and that Wright must have misunderstood any conversation.
"It was questions and answers. I could be tired because I get up early in the morning and I finish late at night, so I am tired, yes. But I didn't give any indication about my future.
"There were many people there. We (he and Wright) had a little dinner before but it was not the two of us. There were four or five."
Asked if Wright could have misinterpreted any comments, he said: "Yes. You know I appreciate very much that you want me to rest, absolutely. But I am not ready for that yet."
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If Arsenal had not won against lowly Hull, it would have ramped up the pressure on Wenger to depart.
Although not at their best, Wenger was pleased to put the recent defeats to bed ahead of a trip to face Bayern Munich in the Champions League last first leg next week.
Sanchez's opening goal was controversially allowed to stand despite the forward handling the ball on its way into the net.
The Chilean wrapped things up with a late penalty following a handball by Sam Clucas that earned the Hull midfielder a red card.
"It was more about the mathematics than about the brilliance today because we had absolutely to win," Wenger said.
"We were playing a bit more to not concede a goal and that's what the game was about because we knew that was absolutely vital to win today."
Hull defender Andy Robertson claimed after the game that referee Mark Clattenburg apologised to Hull's players for not ruling out Sanchez's first goal.
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