When asked whether he would fire Mueller such an investigation, Trump was noncommittal.
Following Trump's victory in the 2016 election, his daughter and her husband became part of the presidential administration.
Mueller's office declined to comment to NBC News for its story.
Russian Federation has denied interfering in the election, and Trump has said there was no collusion.
"I suppose the best case for Kushner is that this looks absolutely bad", Rob Weissman, president of Public Citizen, told the AP.
Vehicle bomb in Afghan capital kills young girl, wounds 19
On Thursday, Taliban fighters killed at least six policemen in an attack at a checkpoint in southern Afghanistan, officials said. He added that the militants have suffered heavy casualties under the new US strategy of increased airstrikes and commando raids.
Church of Holy Sepulchre to reopen doors after protest
They also were protesting a "discriminatory and racist bill" which would allow church property to be claimed by the state. Adeeb Joudeh, the custodian of the keys, said that the church was reopened to the public at 4am local time (02:00 GMT).
Ramaphosa Sworn In As New South Africa President
Zuma fired Nene as finance minister in December 2015, replacing him with unknown parliamentary backbencher Des van Rooyen. During his maiden State of the Nation Address, Ramaphosa said that he would be cutting down his cabinet.
Witnesses and others close to Mueller's probe told NBC News that investigators have been asking about Kushner's business discussions with Turkish, Qatari, Russian, Chinese and Emirati nationals during the presidential transition.
The NBC News story noted that the White House previous year backed an economic blockade imposed on Qatar by Saudi Arabia and the UAE in the weeks after the collapse of talks that the Kushner Companies had with Qatari officials about their sovereign wealth fund investing in a Kushner building in New York City. Yet aides also noted that Mr. Trump has told the couple that they should keep serving in their roles, even as he has privately asked Mr. Kelly for his help in moving them out.
The Kushner Companies' Fifth Avenue property is facing some $1.4 billion in debt that is due in 2019, NBC News cited the sources as saying.
Former U.S. and global officials say that even if Kushner stays, his job won't be the same.
On Tuesday, The Washington Post reported that officials in China, the United Arab Emirates, Israel, and Mexico pinpointed Kushner's senior ranking in the Trump administration, his troubled financial dealings, and his lack of government experience as an opening for political influence.
It is against US law for a government official or someone being considered for a government advisory post to provide advice based on financial interests.