"You are a true fighter, Orrin," Trump said. "You meet people who you thought were fighters -- but they're not so good at fighting. He's a fighter. We hope you will continue to serve your state and your country in the Senate for a very long time to come."
Hatch would be up for re-election next year, and sources close to him have consistently said to expect a decision around the end of the year.
If re-elected, Hatch would have two years remaining as the top Republican on the Finance Committee, under the Senate GOP conference's internal rules. He has suggested that might be an incentive to run again.
In the immediate term, Hatch has plenty on his plate. He will be the Senate negotiator in the conference with the House on overhauling the tax code, an effort for which he drew praise from Trump on Monday.
"I want to especially thank you for the tremendous work in ushering massive tax cuts and reform through the Senate. Just happened, and we have a final step to go. And I predict we're going to be very successful," Trump said. "We're talking about massive, massive tax cuts."
And on completion, the tax code overhaul will inevitably require a number of technical corrections that will keep Hatch and his committee busy.
Hatch also finds himself in the middle of the debate over reauthorizing the Children's Health Insurance Program. Unlike the particularly partisan tax reconciliation effort, the Utah lawmaker already drafted and moved through the Finance Committee a bipartisan reauthorization bill with ranking Democrat Ron Wyden of Oregon.
If Hatch opts not to run next year, 2012 GOP presidential nominee Mitt Romney might seek the seat. Asked about that prospect Monday, Trump said, "He's a good man. Mitt's a good man."
Steve Bannon, the former senior White House adviser and Trump strategist who has returned to Breitbart News, is reportedly mulling his own endorsement of Hatch to help thwart a Romney candidacy.
"If Steve had a choice between Orrin Hatch and Mitt Romney, he would pick Hatch 10 times out of 10," a source close to Bannon told the Washington Examiner.