Washington DC - Federal prosecutors have questioned Donald Trump's son-in-law and ex-advisor Jared Kushner as part of their probe into the former president in the aftermath of the 2020 election, according to media reports.

Kushner has testified before a grand jury, the New York Times and CNN reported on Wednesday. CNN also reported that Trump's close confidant and adviser at the time, Hope Hicks, had been questioned.

The New York Times reported that Kushner had been questioned in June. Both his questioning and that of other witnesses in recent weeks had focused on whether Trump had privately acknowledged that he had lost in the days after the election.

The New York Times said prosecutors are trying to establish whether Trump attempted to remain in power with corrupt intent, that he knew that his claims were based on a lie.

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According to the New York Times, Kushner testified that he had the impression that Trump actually believed that his election victory had been "stolen" – that his successor, President Joe Biden, had not won legitimately.

On the day the Democrat's election victory was to be certified in the US Congress, Trump supporters violently stormed the Capitol building to prevent the transfer of power, after an inflammatory speech by the outgoing president. Trump still refuses to publicly admit defeat.

The US Department of Justice appointed independent Special Prosecutor Jack Smith in November to oversee investigations into Trump. Smith is responsible for the investigation into the events after the election, including Trump's role in the storming of the US Capitol on January 6, 2021.

He also led the investigation into Trump's handling of classified government documents, which has already led to the impeachment of the ex-president.

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The nation is watching intently, waiting for the conclusions of Smith's investigation into Trump's role in the Capitol attack, and to find out whether charges will be brought and, if so, on what offenses.

Kushner, like his wife Ivanka Trump, the former president's daughter, was a close White House adviser to the former Republican president. US media had reported on the subpoena of Kushner and Ivanka Trump in February. According to the New York Times, Trump's daughter is yet to be questioned.