The flag in question was the American flag, but flown upside-down; a gesture reportedly adopted by supporters of Donald Trump after he lost the 2020 election to Joe Biden.
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The photo obtained by the New York Times shows the flag at the Alexandria, Virginia home of Justice Alito.
"That upside down flag was a symbol of 'the big lie': The attempt to steal the election and not admit that Joe Biden was elected," Durbin said.
READ MORE: Photo of upside-down flag at Supreme Court Justice Samuel Alito's house raises concerns: Report
With two cases coming before the high court involving January 6 rioters, and former president Trump's claims of presidential immunity, Durbin is calling for Alito to resuse himself.
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"It's time for him to do two things. First, a clear explanation of what happened and secondly, recuse himself from any case involving President Trump and his immunity from prosecution," said Durbin, who is the chair of the Senate Judiciary Committee.
Alito told the New York Times "I had no involvement whatsoever...It was briefly placed by Mrs. Alito in response to a neighbor's use of objectionable and personally insulting language on yard signs."
Arkansas Republican Senator Tom Cotton responded on social media to the story, saying, "This is the NYT trying to smear Mrs. Alito and incite another mob to try to intimidate justices, harass them at home, or worse. Shameful!"
One of Alito's neighbors did recall seeing the flag around the time Biden won the election.
"I was driving, coming down towards my house. I saw something strange on his flag post. Well in my mind, I just said 'there's something wrong with the flag,'" neighbor Aija Karlson told ABC News.
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According to the U.S. Flag Code, flying the American flag upside down is only meant to be done "as a signal of dire distress in instances of extreme danger to life or property."
Despite the controversy, ABC7 legal analyst Gil Soffer said it's unlikely Alito will step aside.
"And he's clearly making the argument that it was his wife who put the flag up that can't be attributed to him. There's no reason for him to recuse himself. And if that's his final decision, that is a final decision," Soffer said.
The White House said that President Biden would not comment on the calls for Justice Alito to recuse himself, but said the President "feels the American flag is sacred and we should be respecting the flag."