City beat Palace 2-1 whilst Birmingham won 4-1 at Millwall in the Third Round yesterday.
The last FA Cup meeting saw City beat Birmingham in the FA Cup in January 1981 with a 3-2 win at Highfield Road but in the only other FA Cup tie, they lost 5-1 at St Andrews in January 1935.
The tie is expected to take place on Saturday January 29th and will be subject to the demands of television and the FA website who also have broadcasting rights as well as the poilce due to the fact that Aston Villa have been drawn at home to Blackburn Rovers.
If City's Cup tie is played on the Sunday then there is the possibility that the league game against Nottingham Forest could be put back 24 hours.
Ticket news will appear on this site when it is available.
Travel directions to St Andrews can be found by clicking on:
http://www.coventrycity-mad.co.uk/feat/ed14/january_2011_directions_611819/index.shtml