Jared Kushner and Ivanka Trump
Jared Kushner and Ivanka TrumpReuters

US President Donald Trump quietly asked Chief of Staff John Kelly to encourage son-in-law Jared Kushner and daughter Ivanka Trump to leave their White House positions, The New York Times reported.

The Times also said that to their faces, Trump told the couple to remain in their positions.

"In private conversations, the president vacillates between sounding regretful that Mr. Kushner is taking arrows and annoyed that he is another problem to deal with," the Times wrote.

Last week, Trump praised Kushner, saying he's "done an outstanding job."

"I think he’s been treated very unfairly. He’s a high-quality person," Trump added.

However, according to the Daily Mail, Ivanka and Jared have no intention of leaving their posts.

The Hill quoted an unnamed source close to the White House as saying that Kushner is "digging in." The source also said that "Ivanka has made the decision she is not leaving the building and Jared is not going to leave Ivanka in the building alone."

Meanwhile, CNN quoted Kelly as expressing frustration with Ivanka, saying, she "tries to have it both ways, acting as a senior adviser to the president when it suits her and then as his daughter when it doesn’t."

A White House official who spoke with Trump on the topic said the President "was angry that Kushner - and, by extension, daughter Ivanka - were in his view being dishonestly maligned. But he also mused this week that everything might be better for them if they simply gave up their government jobs and returned to New York," the Washington Post reported.

PEOPLE quoted an inside source as saying, "If they leave they’ll be happy to go back to their old lives. They love their kids so much and this is so distracting, to be a young family and have all this pressure instead of focusing on the kids. But now Jared’s name will be tarnished, which sucks for them."

Last week, Ivanka, Kushner, and 30 other White House staffers had their security clearance downgraded from "top secret" to "secret."