Boris Johnson promised in January to draw up proposals for change to the perennially cash-strapped system by the end of this year and to drive them through by the time of the next election in 2024.
But Mr Hancock told the daily coronavirus briefing in 10 Downing Street that the unexpected pandemic had knocked preparations off course, meaning it will not be "straightforward" to meet the prime minister's target.
He said: “Well, the time frame has been clear, which is that we have got to get these reforms done in this parliament and the prime minister has previously said we will get them set out this year.
“That was before coronavirus – we will still try to do that but it is not straightforward.”
On his arrival at 10 Downing Street in July last year, Mr Johnson claimed to have a ready-to-go rescue package to resolve long-standing problems with the funding of social care for the elderly and long-term sick.
But the Conservative manifesto for last December's general election ducked the issue, promising only to seek cross-party consensus, in an apparent attempt to avoid seeing the threat of new taxes to pay for a cap on care costs derail Mr Johnson's campaign as it did Theresa May's in 2017.