On July 18, the US president sued the Journal and its owners, including Murdoch, over a story, which said Trump's name was on a birthday greeting for late sex offender Jeffrey Epstein, that included a sexually suggestive drawing and a reference to shared secrets.
"I've been treated badly by the Wall Street Journal. I would have assumed that Rupert Murdoch controls it, but, you know, maybe does, maybe doesn't," Trump told reporters aboard Air Force One.
"They are talking to us about doing something but we'll see what happens. Maybe they would like us to drop that, so we'll see... yeah, they're having, they want to settle it," he said, adding, "when I get treated unfairly, I do things about it."
Trump's lawsuit called the alleged birthday greeting "fake" and said the Journal published its article to harm the president's reputation.
In a court filing on Monday, Trump asked a US court to order a swift deposition for Murdoch.
Trump's lawyers argued that Murdoch should be asked to depose swiftly, noting that he was 94 and "is believed to have suffered recent significant health scares".
The Wall Street Journal did not immediately respond to a request for comment.
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