Story updated 18/02/2013, 23:00
The sixth-round draw took place at Wembley Stadium on Sunday 17 February and paired the winner of Monday's match with either Boro or the Blues, who will play their fifth-round tie later than everyone else on Wednesday 27 February.
If Middlesbrough win, they will contest their fifth FA Cup tie with United during Sir Alex Ferguson's reign. The Reds were victorious in the 1999, 2005 and 2007 meetings, the latter after a replay, while the Teessiders triumphed in 2002.
Chelsea's last FA Cup clash with United was the 2007 final, when an extra-time goal by Didier Drogba snatched glory for the West Londoners, then managed by Jose Mourinho. The Reds beat the Blues emphatically, 4-0, in the 1994 final and knocked them out of the competition in 1996 (semi-final), 1998 (third round) and 1999 (quarter-final).
This season's quarter-final ties are scheduled to be played on the weekend of 9 and 10 March. This means the Reds' away league game at West Ham will have to be rearranged.