"It has never been easy for me to play well from the start on clay", admitted Sunday evening the 26-year-old Russian, who missed the start of the season on this surface and remains on a defeat in the quarter-finals end of March in Miami.
Appeared diminished during this meeting, the Muscovite had revealed that he had suffered from a slight hernia for several months and had opted for surgery, which had cast doubt on his participation in the French Open.
But Medvedev, world No.1 for three weeks in early March before giving up his place to Novak Djokovic, said he felt "physically good", "ready" to face the winner of the round of 16 between the French Richard Gasquet and the Australian John Millman.
"Even a single tournament will be a good way to prepare," said the Russian.
"From what I can see, the conditions are getting closer to Roland-Garros, where the balls are flying and the ground is quite hard."
Exempted from the first round, he hopes to "play one, two or three matches here" to be physically ready to face next week's best-of-five-set encounters at the Paris tournament.
The participation of Medvedev, and more broadly of Russian and Belarusian players, remains for the time being authorized at Roland-Garros, unlike Wimbledon where the British tennis authorities have banned them due to the invasion of Ukraine.
Other Geneva Open headliners include incumbent winner Casper Ruud of Norway, Canadian Denis Shapovalov and American Reilly Opelka, as well as 2020 US Open winner Dominic Thiem of Austria.
© 2022 AFP