Medvedev, who has finished as runner-up at three other Grand Slam tournaments, has been eliminated from the opening round at Roland Garros in four of his six visits to Paris.
For the 23-year-old Wild, who is currently ranked No. 172 in the world, Tuesday's test against Medvedev will be only the second time that the Brazilian has competed at a Grand Slam, after losing in straight sets to Daniel Evans in the opening round at the 2020 US Open.
Indeed, Wild is clearly developing as a serious player on the red dirt having won 36 of his 46 matches on that surface so far this season, with his only ATP Tour triumph coming against last year's French Open finalist Casper Ruud at the Chile Open three years ago.
However, there is little doubt that Wild's forthcoming meeting against Medvedev will represent one of the toughest challenges of his career so far, but the fact that he is playing on his best surface provides him with a glimmer of hope in terms of inflicting a major upset.
Despite Medvedev undoubtedly being at his most comfortable on a hard court, the Russian will head into the French Open full of confidence after winning the first major clay court title of his career at the Italian Open last week.
Medvedev lost just one set across six matches at the prestigious ATP Masters 1000 event, which has been dominated by Rafael Nadal and Novak Djokovic since the Spaniard won the competition for the first time in 2005.
Indeed, Medvedev joins Alexander Zverev - who he defeated in the third round last week, before taking down Stefanos Tsitsipas and Holger Rune at the latter stages - and Andy Murray as the only other players to have won the Italian Open across those two decades.
As such, with 14-time Roland Garros champion Nadal forced to withdraw from this year's competition due to an ongoing hip injury, it is little surprise that Medvedev's odds to win the French Open outright have been slashed with most bookmakers since his surprising triumph in Rome.
While that may be a tall order for a man who has only made it beyond the first round of the French Open on two occasions, the 27-year-old is entering the peak of his career and clearly has the mental fortitude and technical ability to go all of the way this time around.
Head To Head
Seyboth Wild and Medvedev are yet to meet in their respective careers, making Tuesday's meeting their first one. As such, we have no head-to-head data to report on.
We say: Medvedev to win in 3 sets
Although Wild is unlikely to make it easy for Medevdev having enjoyed an excellent clay court season by his own standards, the Russian will be full of confidence after his recent triumph at the Italian Open.
The US Open champion has never been a natural performer on the red dirt, but having finally prevailed at a major clay court tournament, he will fancy his chances in the absence of Nadal this year.