Brendan Rodgers' side overcame Bournemouth 3-1 in the last eight on Wednesday, and will now face the current Premier League leaders over two legs in the new year.
Chelsea also prevailed 3-1 against Championship opposition, as they triumphed against Derby County on Tuesday.
The two sides contested the final of this competition in 2005, when Chelsea emerged 3-2 victors after extra-time having found a late equaliser through Steven Gerrard's own goal.
The other tie sees Spurs take on League One outfit United, who provided the shock of the quarter-final round by seeing off Premier League Southampton 1-0 at Bramall Lane.
Tottenham won this competition as recently as 2008, and booked their place in the last four this time with a 4-0 thrashing of Newcastle United at White Hart Lane.
United, have only once before reached this stage, in 2003 - but they have good cup pedigree having reached the final four of last season's FA Cup before falling to Hull City 5-3 at Wembley.
The first leg ties are due to be played during the week commencing January 19, with the return fixtures scheduled for the following week.
