The repeat of last year's final was due to be screened at the BBC's primetime slot of 7pm on Sunday 27 January.
But after crowd violence marred the weekend's third-round programme at Cardiff's game with Leeds, as well as the pitch invasion at Aston Villa's match with Manchester United, police and the Football Association are not leaving anything to chance and ongoing discussions are considering a possible 1pm start.
The Metropolitan Police has a policy of preventing London clubs from staging Sunday evening games because of the likelihood that supporters would start drinking at lunchtime.
That policy is to be adhered to, despite representations from the BBC, who wanted to show the Highbury game in their new showcase Sunday evening spot.
The Met Police has particular concerns about the fourth-round fixture programme because of the potential for six ties in London over the Cup weekend.
Charlton, Millwall, Tottenham, Chelsea, Wimbledon and Arsenal could all be at home if they come through postponed third-round matches and replays over the next two weeks.
A police spokesman said: "We have an agreement that we don't do 7pm on a Sunday throughout London.
"We have been in discussions with the FA which knows that we can do 12pm, 2pm or 4pm instead. There are a lot of complex issues to be sorted out because there could be so many teams in London on the same day."