“Absolutely no one flying the flag of Russia should be allowed or engaged,” Huddleston said.
“We need a possible assurance that they are not supporters of Putin and we are considering what requirements we need to try and get assurances in that direction.”
Huddleston said he was in contact with the tournament’s organizers, the All England Lawn Tennis Club (AELTC), and talks were underway.
DailyExpertNews has contacted the AELTC but has not received an immediate response.
The current rules allow Russian and Belarusian players to participate in the ATP and WTA women’s tour, but only as neutral athletes.
Russia and Belarus, which helped invade Ukraine, have been barred from team events such as the Davis Cup and the Billie Jean King Cup as the sport continues to turn its back on Putin.
“My message is always the same: I want peace in the whole world,” Medvedev told reporters earlier this month when asked about the war.
DailyExpertNews contacted Medvedev’s team about Huddleston’s comments, but received no immediate response.
However, WTA head Steve Simon said he doesn’t want players banned if they don’t publicly criticize the “decisions of an authoritarian leadership”.
“You never know what the future will bring,” Simon told the BBC on Tuesday.
“But I can tell you that we have never banned athletes from taking part in our tour because of the political stances their leadership might take.
“So it would take something really important to change that, but again, we don’t know where this is going.”
The WTA would have to change its rules if the government decided to ban Russian players, but Simon said it would not be a move he supports.
“I strongly believe that these individual athletes should not be the ones who are being punished by the decisions of an authoritarian leadership that is clearly doing terrible, reprehensible things.”
Wimbledon is scheduled from June 27 to July 10.