Medvedev, who went out in the first round of the French Open last month, won the first set before going down 4-6, 6-4, 6-2 to the 52nd-ranked Mannarino, who won the Dutch tournament in 2019.
Mannarino will play former Wimbledon finalist Milos Raonic, returning to the tour after nearly two years out with injury, or Australian Jordan Thompson in the quarterfinals.
Medvedev, winner of a tour-leading five titles this season, will be in action next week in Halle, Germany – another grasscourt tune-up event ahead of Wimbledon.
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