Elsewhere, world number one Jannik Sinner said he had “a few sleepless nights” after losing to Carlos Alcaraz in the French Open final.
The Italian held three championship points in the third set but lost to world number two Alcaraz in a five set, five-hour epic at Roland Garros.
Sinner will begin his grass-court campaign at the Halle Open on Monday.
“I think every day it gets better,” Sinner said.
“Tennis is important in my life but family and friends are more important.
“I was very relaxed with my family. We grilled a bit, played table tennis with my friends.
“Nonetheless, I think often about the match.”
Sinner will be joined by fellow top-20 players Zverev, Daniil Medvedev and Andrey Rublev in Halle.
Meanwhile two-time defending Wimbledon champion Alcaraz will begin his grass-court season at Queen’s, where he won the title in 2023, along with Britain’s Jack Draper.
Nine of the world’s top 10 women’s players will compete in the Berlin Open, including French Open champion Coco Gauff, world number one Aryna Sabalenka and world number three Jessica Pegula.
British number one Emma Raducanu withdrew from the event on Saturday as she continues to manage a back problem.