"Many countries around the world have agreed that we will not allow representatives from Russia to compete and there are visa implications here as well."
The Times reports Wimbledon organisers and officials from the other grand slams have discussed the possibility of extending sanctions to Russian and Belarusian players that go beyond what has already been imposed by the ATP, WTA and ITF amid the invasion of Ukraine.
Tennis reporter Stuart Fraser tweeted: "Understand that some Wimbledon officials have concerns about the optics of allowing Russians to play in this summer's championships, when other sports have taken more drastic action. Discussions with other grand slams have taken place in recent days."
Tennis' governing bodies decided earlier this moth Russian and Belarusian players could still compete, but not under the name or flag of their homeland. The ITF also suspended both countries from team events, the Davis Cup and Billie Jean King Cup, and the ATP and WTA tournaments set to be held in Moscow in October have been suspended.
Medvedev, who lost this year's Australian Open to Rafael Nadal, posted on Instagram a couple of weeks ago asking for "peace in the world" and "peace between countries", but stopped short of openly condemning Russia's invasion of Ukraine.
After winning her round one match at Indian Wells on the weekend, Ukrainian star Marta Kostyuk lashed out at Russian tennis players for not making a big enough statement about the atrocities being committed in her country.
"You cannot be neutral in this," Kostyuk said. "These 'no war' statements — they hurt me because they have no substance.
"Seeing (Russian) players on-site really hurts me. And seeing them having the only problem not being able to transfer the money and stuff — that's what they are talking about — this is unacceptable for me.
"What is very disappointing is that no Russian player came to see me. None have told me they're sorry for what their country is doing to mine.
"One player messaged me, another chatted with me, but I didn't hear any apologies, I didn't hear anyone telling me they didn't support what was going on. To me, that's shocking.
"You don't have to be involved in politics to behave like a human being. Everyone knows what's going on. It hurts me. It hurts me every time I arrive at the stadium and see all these Russian players."