Yes.The more than 20 existing GCMs predict gridded climate fields of SSTs, so from here you can construct the average anomalies for which Niño 3.4 is defined in 20W-170W, 5N-5S
The International Research Institute for Climate & Society (IRI) collects, posts, and distills ~25 ENSO predictions into a probabilistic outlook on ENSO. We also are a leading contributor to the WMO ENSO Outlook. For the most recent outlook, produced by IRI and the Climate Prediction Center (within the National Weather Service), check this link: http://iri.columbia.edu/our-expertise/climate/forecasts/enso/2013-september-quick-look/#
The October outlook should be available in a week or so.