“Absolutely no one should be allowed or able to fly the flag for Russia,” Huddleston said.
“We need some possible reassurance that they are not supporters of Putin and we are looking at what requirements we might need and get some reassurance along those lines.”
Huddleston said he was in contact with the tournament’s organisers, the All England Lawn Tennis Club (AELTC), and that discussions were taking place.
CNN contacted AELTC, but did not receive an immediate response.
Current rules allow Russian and Belarusian players to compete on the men’s ATP and women’s WTA tours but only as neutral athletes.
Russia and Belarus, which helped invade Ukraine, have been banned from team events such as the Davis Cup and the Billie Jean King Cup as the sport continues to turn its back on Putin.
When asked about the war, Medvedev told reporters earlier this month: “My message is always the same – I want peace all over the world.”
CNN contacted Medvedev’s team about Huddleston’s comments, but did not receive an immediate response.
However, WTA chief Steve Simon said he does not want players to be banned if they do not publicly criticize “the decisions of an authoritarian leadership”.
“You never know what the future may bring,” Simon told the BBC on Tuesday.
“But I can tell you that we have never banned athletes from participating on our tour because of the political situation that may result from their leadership.
“So it will take something very important to change, but again we don’t know where it’s going.”
If the government decides to ban Russian players, the WTA will have to change its rules, but Simon said it would not be a move he supports.
“I feel very strongly that these individual athletes should not be punished by the decisions of an authoritarian leadership that is clearly doing horrible, reprehensible things.”
Wimbledon is scheduled to run from June 27 to July 10.