Mr Mueller is looking into any links between Russia and the Trump campaign.
Both deny there was any collusion.
Mr Flynn was forced to resign in February after misleading the White House about meeting the Russian ambassador before Mr Trump took office.
The meeting between Mr Kushner and Mr Mueller's team lasted less than 90 minutes, reports said.
In a statement, Mr Kushner's lawyer Abbe Lowell said: "Mr Kushner has voluntarily cooperated with all relevant inquiries and will continue to do so."
Mr Kushner has previously admitted initially failing to disclose contacts with Russians.
Earlier this month Mr Flynn's lawyers reportedly told Mr Trump's legal team they could no longer discuss the Russia investigation.
The move suggested Mr Flynn may be cooperating with Mr Mueller's investigation, US media said.
The controversy surrounding alleged Russian interference in last year's election has hung over the Trump administration since earlier this year, when US intelligence agencies said the Russian government sought to help Donald Trump win.
Congressional committees were set up to investigate the matter and in March the FBI said it was conducting its own inquiry.
President Trump later sacked FBI director James Comey, citing his reason as "this Russia thing", in a move that shocked Washington and fuelled claims of a cover-up.
However, it did not halt the investigation. In May the department of justice appointed Mr Mueller as special counsel to look into the matter.
In October it was reported that the first charges had been filed in the investigation.
The investigation has also led to a separate allegation against Mr Flynn. The Wall Street Journal reported that he was part of a plot to help forcibly remove a Muslim cleric to Turkey, something he denies.
Earlier this year it emerged that Mr Flynn failed to register as a lobbyist for the Turkish government while he was seeking White House security clearance.
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