Chelea would visit Championship side Middlesbrough in the quarter-finals of the FA Cup, in a rematch of the 1997 final, while Manchester City would travel to Southampton in the only confirmed All-Premier League tie.
In other ties, Crystal Palace will host the winners of Thursday's fifth round matchup between Everton and Boreham Wood, while Liverpool will move to Nottingham Forest or Huddersfield Town. The two championship clubs will face each other in the final fifth round match on Monday.
The quarterfinals will be played over the weekend of March 18-21 and all games will be live on ESPN+ in the US.
Chelsea have been regular visitors to Wembley in recent years, reaching the FA Cup final in four of the last five years, though winning only one of those occasions. They will have fond memories of Middlesbrough, who won over the same opponents at Old Wembley 25 years ago, but will be wary of a side that has already ousted Manchester United and Tottenham ahead of this season's competition.
With a visit to Premier League Crystal Palace on the horizon, the draw provides further inspiration for non-league outfit Boreham Wood if they can continue their story by ousting Everton.
Meanwhile, Liverpool would love their chances of continuing their search for a historic quadruple as they seek a first FA Cup trophy under Jurgen Klopp.
With Chelsea, Liverpool and Manchester City avoiding each other in the last eight, it sets up the possibility of a heavyweight semi-final lineup if all are formed later this month.
FA Cup quarter final draw
Crystal Palace vs Everton or Boreham Wood
Nottingham Forest or Huddersfield Town vs Liverpool
Middlesbrough vs Chelsea
Southampton vs Manchester City