It was found that the oVirt web admin interface stored session IDs in HTML5 local storage. A remote attacker could provide a specially crafted web page that, when visited by a user with a valid REST API session, would allow the attacker to read the session ID from local storage. This is possible because HTML5 local storage is not protected by the same-origin policy (SOP).
Note that the RESTAPI doesn't store the session IDs anywhere, it is the client that does so, in this case the UI. I have changed the component in the tracking bugs accordingly.