The meeting between Mr. Trump and SkyBridge Capital managing partner Anthony Scaramucci, a national finance co-chairman of Mr. Walker’s campaign, comes after the celebrity businessman began attacking hedge-fund operators, who Mr. Trump said Sunday are “getting away with murder.”

“He wants to drop Walker and go with me,” Mr. Trump said in a phone interview Monday. “He wants to endorse me. He said, ‘I want to drop Walker and endorse you.’”

Mr. Scaramucci said the two discussed the possibility of his defecting to Mr. Trump but said he told Mr. Trump it wasn’t possible.

“What I said to him again today is that I love him as a guy, but I’m loyal to Scott Walker,” Mr. Scaramucci said in a phone interview. “That does not detract from my friendship with him, but can he please stop railing on the hedge-fund industry?”