Washington (CNN) Rudy Giuliani said Sunday that special counsel Robert Mueller is aiming to finish the probe into potential wrongdoing by President Donald Trump by September 1.

Giuliani, Trump's attorney, confirmed to CNN that Mueller's office shared its timeline with him about a month ago.

The former New York mayor said, however, that Mueller gave him the information within the context of a discussion about whether Trump would do an interview with the special counsel. Giuliani said the impression he got was that Mueller was saying if the President did do an interview, then the investigation into Trump's actions, including any potential obstruction of justice or possible collusion with Russia's interference in the 2016 election, could be wrapped up by that date.

Giuliani told CNN that he did not see Trump doing an interview with Mueller unless he had access to details about a confidential FBI source that spoke with some aides to Trump's presidential campaign about its possible ties to Russia.

Trump has suggested the source was planted in the campaign to spy on it -- something US officials have told CNN is not the case -- and on Sunday demanded his Justice Department look into whether anything like that occurred for political reasons.

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