Lincoln, who beat Burnley in the fifth round, are the first non-league team in 103 years to reach the last eight.
Elsewhere holders Manchester United travel to Premier League leaders Chelsea.
Millwall, who beat Leicester, will play Tottenham.
Non-League Lincoln are in the draw for the FA Cup quarter-final draw
Middlesbrough will face either Manchester City or Huddersfield, who drew 0-0 on Saturday.
The ties to be played on the weekend of the 10-13 March.
Arsenal all smiles in training ahead of Sutton showdown
Sun, February 19, 2017
Express Sport brings you all the best snaps as Arsenal train ahead of their FA Cup clash with Sutton United
Arsenal FC via Getty Images
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Arsenal have been training ahead of their FA Cup clash with Sutton United
Chelsea v Manchester United
Middlesbrough v Huddersfield/Manchester City
Tottenham v Millwall
Sutton/Arsenal v Lincoln