Nadal was barely troubled on Monday as he eased to a 6-1 6-2 6-1 victory over young Serb Dusan Lajovic.
The world number one, an eight-time French Open champion, took just over an hour and a half to complete a record 32nd win in succession at Roland Garros.
However, he can expect a sterner test from fifth seed Ferrer, who booked his place in the last eight by beating Kevin Anderson 6-3 6-3 6-7 (5-7) 6-1.
Ferrer was beaten in straight sets in the 2013 final and has won only six of 27 previous ATP Tour meetings against Nadal.
However, Ferrer was victorious when the two met in the quarter-finals of the Monte Carlo Masters earlier this year.
Andy Murray and Gael Monfils also secured quarter-final berths on Monday.
Wimbledon champion Murray showed no ill effects following his marathon five-set battle with Philipp Kohlschreiber, beating Fernando Verdasco 6-4 7-5 7-6 (7-3).
Murray was made to work hard by the 24th seed, but broke at key points in each of the first two sets before coming through a tie-break to round off his victory.
Monfils kept hopes of French success alive with a convincing 6-0 6-2 7-5 win over Guillermo Garcia-Lopez.
The number 23 seed demonstrated devastating form in the opening two sets as his opponent only won 24 points.
Garcia-Lopez did his best to fight back, but could not avoid a straight-sets defeat.