Egypt, Japan, Spain, New Zealand and Uruguay are working on the measure which would reaffirm that such attacks violate international law and would call for perpetrators to be held accountable.
All five are non-permanent members of the 15-nation Security Council.
"Given the increase of attacks, it would be timely to have a text that holds up international law, re-states respect for medical workers and sends a message about health care in armed conflict," said New Zealand's UN mission spokeswoman Nicola Garvey.
The United Nations has raised alarm over the targeting of medical workers and hospitals in conflict zones, in particular in Syria, Yemen and Afghanistan.
Last year, there were 94 attacks in Syria against 63 hospitals and clinics supported by Doctors Without Borders (MSF), according to the organization's executive director Jason Cone.
Missile strikes have hit at least three MSF clinics in Yemen, where a Saudi-led coalition has been battling Shiite Huthi rebels who have seized territory from the internationally recognized government.
One of the most devastating attacks was the US strike in October on a MSF-run hospital in the Afghan city of Kunduz that killed 42 people.
MSF condemned the airstrike as a war crime and demanded an investigation.
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The US military unveiled the results of an internal investigation a month later, blaming human error.
- Attacks becoming normal -
MSF is supporting the initiative by the five council members, which would not break new legal ground but would highlight the need to respect existing humanitarian law.
"Unless states come together and denounce these attacks, these kinds of attacks will somehow become normal, acceptable by-products of conflict," Cone told AFP.
The draft resolution is being negotiated at a time when four of the five permanent council members -- Britain, France, Russia and the United States - are backing parties in the Syria conflict.
"There really is a lack of accountability for these attacks," Cone said.
He pointed to inaction from the Bern-based international humanitarian fact-finding commission that is supposed to carry out inquiries of attacks on health care facilities.
The draft resolution could be presented to the 15-member council as early as next week, diplomats said.
Cone described hospital attacks as "an incredibly worrying trend" for MSF, which has also seen its clinics looted and staff threatened in South Sudan and Sudan.
"We don't have any illusions that this will be the only thing that changes this trend but it is part of the denunciation of these trends," he said.