Arsenal is scheduled to host Wolverhampton Wanderers and Chelsea is at home against local rival Fulham, but thousands of fans could struggle to reach the stadiums because of a planned strike by London Underground train drivers.
While most top European leagues take a winter break, the December 26 schedule is a traditional highlight of the English season for many fans.
"We are closely monitoring the situation, together with all the relevant agencies," Arsenal said. "The paramount concern to Arsenal Football Club is the duty of care we have towards the Arsenal supporters, Wolverhampton Wanderers supporters, match day employees and indeed everyone who is planning to attend this match."
Arsenal said it is in contact with London police, transport authorities, the Premier League, Wolves and local government.
Supporters heading to matches are already hindered by the fact that overground rail services in Britain do not run on December 26, a national holiday.
"A proposed industrial strike on London Underground, combined with the lack of national rail services in operation could make reaching the stadium difficult both for Chelsea and Fulham supporters," Chelsea said.
The games would be the second and third postponed in London this season. Tottenham was forced to cancel its August 13 home match against Everton because of the local disorder that sparked a wave of rioting and looting across England.
That match has been rescheduled for January 11.
Last season, Chelsea had to postpone its Premier League match against Manchester United on December 19 because of heavy snow, eventually playing the game almost four months later. Seven of the 10 Premier League matches were postponed that weekend because of the snow.
