The Israeli newspaper Yedioth Ahronoth said that Musk may travel to Israel next week, where he is scheduled to visit Kibbutz Be'eri on the border with the Gaza Strip, which was attacked by Hamas on October 7.
Malik X is also expected to meet with Israeli Prime Minister Benjamin Netanyahu and President Isaac Herzog.
"Visiting Israel could help Musk improve his reputation after being accused of anti-Semitism," the source said.
Accusations of anti-Semitism have dogged Elon Musk in recent days after pro-Hitler and Nazi posts appeared on the X platform.
The US billionaire also responded to a post saying that "Jews are using against whites the same hatred that they are asking people to stop using against them," and Musk commented: "I have already told the truth."
The White House condemned what it called Musk's "hateful promotion" of anti-Semitism.
The European Commission also said: "We have seen an alarming increase in disinformation and hate speech on many social media networks in recent weeks, and this of course includes the X platform."
Musk has also sparked controversy after giving his opinion on Israel's war on the Gaza Strip, saying in an interview with broadcaster Alex Friedman: "If you are committing genocide against an entire people, you will leave behind many living people who will be haters of Israel."
On Tuesday, Musk announced that X would donate everything from advertising and subscriptions related to the war in Gaza to hospitals in Israel and the Red Cross and Red Crescent in Gaza.