The hospital is to be set up in the central Golan Heights or near the Quneitra border crossing with Syria, the report Monday said. No timeline for when the hospital would be operating was mentioned.
The Israeli army didn't confirm the report.
The decision comes days after seven injured Syrian refugees were taken to a hospital in Israel for treatment after they were spotted by Israeli soldiers near the border.
At the time, the Israeli army said the incident was an isolated one, based on humanitarian assistance, and didn't reflect a change in policy that might allow refugees fleeing Syria to enter Israel.
The Israeli army said it fears Israel's treatment of the seven Syrians may encourage a surge of refugees into Israel, the Channel 10 report said. Thousands of Syrians have fled to Lebanon, Jordan and Turkey, since the uprising in Syria began two years ago.
Referring to the Syrians hospitalized in Israel over the weekend, Israeli Prime Minister Binyamin Netanyahu said at Sunday's Cabinet meeting, "We will continue to protect our borders and prevent people crossing or entering into Israel, except for individual, specific cases, each of which will be considered on its own merit."