The president, who was speaking at a news conference at his golf property in Bedminster, New Jersey, gave no details about his plan.
Mr Trump has criticised the cost and coverage under Obamacare and has been promising since his 2016 campaign to replace it with a better plan.
His administration asked the Supreme Court in June to invalidate the Obamacare law.
Joe Biden, the Democratic nominee for the presidential election on November 3, has condemned Mr Trump for fighting to gut Obamacare, accusing him of threatening healthcare protections for millions of Americans in the midst of a raging pandemic.
America’s jobless rate is 10.2 per cent, with an extra 10.6m Americans unemployed compared to before the pandemic.
On Friday in Washington, Trump’s chief of staff, Mark Meadows, and Treasury Secretary Steven Mnuchin said there was no progress in negotiations at the Capitol with the two top Democrats in Congress, House Speaker Nancy Pelosi and Senate Democratic leader Chuck Schumer.
Friday’s talks appeared to mark the end of nearly two weeks of almost daily closed-door negotiations between the four leaders, who have sought to hammer out an agreement on legislation to resume Covid-19 relief programs that expired at the end of July.
Democrats said they offered to reduce a proposed $3.4 trillion coronavirus aid package, which the House passed in May but the Senate ignored, by nearly one third if Republicans would agree to more than double their $1 trillion counteroffer but Mr Trump’s negotiators turned them down.
“It was a disappointing meeting,” Mr Schumer told reporters.
Both sides said they remained open to further negotiations.
“I will be back here any time to listen to new proposals,” said Mr Mnuchin, who identified the roadblocks as funding for state and local governments and an extension of enhanced unemployment payments, a $600 per week lifeline for those who have lost jobs in the coronavirus crisis.
Ms Pelosi said she gave him and Mr Meadows a stern parting message: “Come back when you’re ready to give us a higher number.”