Riots have taken place around the country since Saturday, stretching police resources.
A joint statement from the Premier League and Football League read: "We're in talks with our London clubs, the police and authorities.
"A further statement will be made after the situation is reviewed on Thursday."
There are three Premier League fixtures taking place in London on Saturday, all at 1500 BST: Tottenham v Everton, Fulham v Aston Villa and QPR v Bolton.
Tuesday's statement added that "there is no reason to think any matches outside of London will be affected", but it was released before trouble also flared up in the West Midlands and Manchester.
David Bond assesses the impact on the sporting schedule
West Bromwich host Manchester United on Sunday at 1600 BST before Manchester City play at home to Swansea on Monday at 2000 BST.
Several football fixtures have already been affected by the riots. England's international friendly against the Netherlands on Wednesday was called off, as was Ghana's friendly with Nigeria at Watford's Vicarage Road, which was due to take place on Tuesday.
Tuesday's Carling Cup matches at Charlton, West Ham, Crystal Palace and Bristol City were also postponed.
http://news.bbc.co.uk/sport1/hi/football/14472012.stm