Mr. Zeldin, an outspoken supporter of Mr. Trump, has already raised $2.5 million in campaign cash since announcing his candidacy last month, according to his campaign, and has worked to position himself to gain Mr. Trump’s endorsement.
“It’s clear that Congressman Zeldin has the support, momentum and dogged determination to win and restore New York to glory,” said Ian Prior, a campaign spokesman for Mr. Zeldin.
Mr. Trump made it clear to Mr. Giuliani when they saw each other at Mar-a-Lago, Mr. Trump’s estate in Florida, a few weeks ago that he was leaning toward Mr. Zeldin, according to two people with knowledge of the discussion.
Mr. Giuliani, in the conversation, suggested that the former president wait until after the next campaign filing, in mid-July, so that Mr. Giuliani could demonstrate his viability, the people said.
Mr. Giuliani did not dispute that account. “All I can say is the president has been a friend for a long time and somebody I have been honored to work for,” he said. “I think he is going to be very impressed.”
A confident speaker, Mr. Giuliani made a favorable impression on some Republican Party operatives in meetings before county chairs last month. He is scheduled to travel around the state over the next week, according to his campaign. State party officials had hoped to avoid a primary, but with one now all but assured, they appear to have embraced the energy.
“Rudy will forever be known as the man who transformed New York City, and Andrew can be the one to do it statewide,” said Nick Langworthy, the party chairman, in a statement. “New York is broken and in need of the type of overhaul that the Giuliani administration ushered in during the 1990s.”