The London Underground is likely to be closed if planned industrial action by drivers goes ahead, and there are limited mainline train services in and out of the capital.
Arsenal warned earlier this month they would consider rearranging the derby in the event of a strike.
And a statement on the club website read: "We are currently in discussions with the Premier League, West Ham United, police and relevant authorities over the possible postponement of the Boxing Day fixture.
"The match is in doubt due to the difficulties of getting 60,000 supporters, plus matchday staff and employees to the stadium safely in the advent of disruption to public transport on a public holiday.
"The club will make a further announcement as soon as a final decision is made."
Arsenal put back for 24 hours last year's Boxing Day fixture with Wolves in similar circumstances, but Newcastle are due to visit on 29 December so it would almost certainly be January before the West Ham game could be played.