Palestinians are upset at Jewish settlement clubs in the West Bank playing in Israeli leagues. FIFA could have sanctioned the Israeli football federation but wants to examine the issue further.
FIFA president Gianni Infantino had said dealing with the problem was one of his "top priorities" but there was little movement at the end of a two-day FIFA Council meeting.
FIFA's envoy to the region, South African Tokyo Sexwale, said a final report on the controversy should be ready next month. FIFA will then debate the matter again in January.
The Palestinian fooball federation sees the settlement clubs as illegal and has long urged FIFA to punish the Israeli federation.
FIFA rules bar members from organizing games on another federation's territory without permission.
Sexwale, a former FIFA presidential candidate, said: "We are almost working in the area of extra time."