Mr Trump, who has pledged repeatedly to repeal the 2010 law, signalled he was receptive to a compromise after visiting the White House on Thursday.
He told the Wall Street Journal he favours keeping two pillars of the bill because "I like those very much".
One is a ban on insurers denying coverage for pre-existing conditions.
The other provision that the president-elect told the newspaper he favours allows young adults to be insured on their parents' policies.