https://www.israelnationalnews.com/News/News.aspx/150757
Quote
The Israeli government and the Vatican are deadlocked in discussions over the status of the religious sites. Vatican officials are now reiterating their demand for control over the religious sites in the ancient and holy city founded by King David as the capital of ancient Israel and now the capital of the reestablished Jewish state.
Danny Ayalon, Israel’s deputy foreign minister, declared that Israel might consider giving the Vatican “a greater role” in operating the sites. In the last weeks, the Roman Catholic Church’s authorities increased their political initiatives for Catholic control over some sites in Jerusalem.
End quote
This passage indicate possibility Israel give Vatican control or tule old part of Jerusalem.
Old part of Jerusalem is what they want, so one day pope able to rule from there, imatting jesus that come and rule from the mount of olives