Top White House economic advisor Larry Kudlow said Thursday that President Donald Trump could put forward a tax cut before the 2020 presidential election.

"You very may well see a new rollout of additional middle-class tax relief and small-business tax relief," Kudlow said in an interview on Fox Business Network.

Kudlow stressed that "there is nothing in the near term" because "we believe the economy is quite healthy." "But longer run, why not?" he added.

Kudlow also confirmed to CNBC that he supported a tax cut proposal floated earlier Thursday by Sen. Rick Scott, R-Fla.

"Had a great conversation with my friend @larry_kudlow yesterday about our economy," Scott tweeted Thursday morning.

"When we get back from recess, we should immediately start working on a plan to reduce taxes for middle-class families & workers by the amount the Treasury is collecting in tariffs," the senator said.

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In a text message, Kudlow told CNBC, "I do support the proposal" put forward by Scott in their meeting. Kudlow did not say if he had asked the president about the plan.

A spokeswoman for the Florida senator said that Scott "has not yet spoken to the president on this proposal, but is urging the Administration to start immediately cutting fees to help American families."

Kudlow made similar comments to reporters at the White House shortly after his television interview.

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Kudlow also told Fox that he still expected Chinese negotiators to meet with Trump administration officials in Washington in September to continue trade talks.

The deputies for Washington and Beijing had a "productive conference call" Wednesday, he said.

The remarks from the top economic aide came amid a week of mixed messaging from the White House about possible tax cuts and other proposals to stimulate the economy.

On Wednesday, Trump said that he's "not looking at a tax cut now. We don't need it."

That statement appeared to be completely at odds with the president's comments from just a day earlier, when he said in the Oval Office that he has "been thinking about payroll taxes for a long time."

Less than a day before those comments, a White House official had denied that a payroll tax cut was being considered: "More tax cuts for the American people are certainly on the table, but cutting payroll taxes is not something under consideration at this time."

And that denial came in response to The Washington Post's report that White House officials have been floating a payroll tax cut as a way to head off a possible economic slowdown.

When asked Thursday to provide more details about the possible preelection tax cut, Kudlow said, "I don't want to get in a lot of detail on this because, I don't want to get ahead of the curve."

But he did say that "the idea of some short-term payroll tax cut fix -- it doesn't work, it never works, it has no lasting impact."

He added: "The personal tax rates could easily be lowered, and probably the brackets could be shrunk. That's a thought."

And "we might even kind of work through a way to help our friends in some of the states who are concerned about the shrinkage of the tax deductions there ... the SALT taxes," Kudlow said.

But he cautioned not to take those suggestions as promises. "I'm just -- these are for examples, OK? For examples," he said.