The game is the most likely one that Sky Sports could ask the Premier League to push back from 23rd December to Christmas Eve, which falls on a Sunday, for the purpose of a live broadcast.
It was initially suggested that it would fill the usual 4pm 'Super Sunday' timeslot, but that yielded much criticism from those concerned about the logistics and feasibility of fans, particularly coming from Merseyside, travelling home afterwards.
Premier League chief executive Richard Scudamore has declared this week that no game will kick off at 4pm on Christmas Eve following the backlash. Any game played on Christmas Eve is now expected to be scheduled for a 12pm or 2pm kickoff.
Given his say, Wenger admitted at his weekly press conference that he would rather not kick off any later than 2pm if Arsenal are asked to play on Christmas Eve.
"I know that we have to adapt to the schedule dictated by television, but overall I would say if that, personally, I don't think any games should be played after 2pm on Christmas Eve.
"Personally I would prefer to be at my home and celebrate Christmas, but I still feel that could happen if we played early on [Christmas Eve]," the Frenchman added.
"What you wouldn't like to sacrifice is the evening with family, but overall we have moved towards a society where religion isn't considered in any decisions anymore."
Only once in Premier League history has a game ever been played on Christmas Eve. That came way back in 1995 when Manchester United were beaten 3-1 by Leeds at Elland Road.