Brown told CNN's Jake Tapper on "State of the Union" he's happy with his current job -- even though he plans to help Clinton in the general election.
"I will put real effort into helping to elect Hillary Clinton," the Ohio Democrat said. "As I said, I love this job, and I'm just not going to give you a different answer."
When Tapper pointed out that was no firm denial of interest, a laughing Brown said: "I understand."
Brown is a labor-friendly senator beloved by unions. He's a strident opponent of free trade pacts and some of the tactics -- including currency manipulation to make their products cheaper -- that Trump hammers countries like China and Mexico for on the campaign trail.
But he said Clinton's positions are more likely to help American workers.
He pointed to her criticism of the Trans-Pacific Partnership, a 12-country trade pact negotiated under President Barack Obama, for its failure to address currency manipulation and its rules of origin that govern where product components must be made in order for other countries' exports to qualify for the deal's slashed tariffs.
"Secretary Clinton will work on these trade enforcement issues and will oppose these trade agreements, and (has an) understanding how to do that, in a way that Donald Trump has never really offered," Brown said.
He also attacked Trump more broadly over wages, pointing to the businessman's assertion that they are too high.
"So he's clearly been against the minimum wage," Brown said.
The Ohio senator also cited Trump's opposition to the prevailing wage, which guarantees higher pay on government contracts to laborers, and his support for union-busting "right to work" laws.
"When they see the big picture on jobs, the big picture on manufacturing, the big picture on trade, they're going to see a few shallow words from Trump," Brown said. "But they're going to see a lifelong commitment ... from Hillary Clinton."