The Crown Prince has denied any involvement in the killing.
Despite initially claiming it played no role, Saudi Arabia has admitted a team of rogue operative flew to Turkey and killed Khashoggi.
The CIA has determined that the Crown Prince personally ordered the killing.
However, Trump has thrown his support behind Saudi Arabia, insisting the US has yet to finally conclude who was responsible and talking up the importance of ties with the country in keeping Iran in check.
The reports suggest Kushner was a key voice inside the White House arguing that Saudi Arabia remained a critical part of the president's Middle East strategy.
The relationship has been two years in the making, including a meeting with the Crown Prince's most senior aides in the month when Trump was elected.
A slide obtained by the Lebanese newspaper Al Akhbar apparently reveals the views of a Saudi delegation that visited the US in November 2016.
"The inner circle is predominantly deal makers who lack familiarity with political customs and deep institutions, and they support Jared Kushner," it said.
It appeared to pay off. When Prince Mohammed met Trump at the White House in March last year, Kushner arranged for the kind of media treatment usually afforded only heads of state, according to a source involved in the arrangements.
In a rare interview, Kushner previously said he urged the Crown Prince to be "fully transparent" about the fate of the dead journalist.
The new allegations that the two remained in close contact brought fresh calls from critics of Trump to take a tougher stance.
Marco Rubio, who sits on the Senate foreign relations committee, said the evidence of the Crown Prince's role was clear.
"It is an alliance that has limits, like any alliance would," he said. "This is a crown prince that is a reckless individual."
He added that the relationship came with human rights obligations.
"We cannot be a nation that says when our allies do something horrifying we're going to look away. It is not in our national interest to be a defender of human rights violations," he said.
This article originally appeared on the Daily Telegraph.