Air carrier Dispatcher reported a Captain was reporting the failure of a GPS unit prior to oceanic airspace. The Dispatcher had difficulty convincing the Captain that the aircraft was in a known area of GPS jamming.

Narrative

I received a SATCOM call from the Captain who informed me they were having issues with the left GPS and it wasn't functioning properly. The aircraft kept going into DME DME Mode and his ANP value was going up and was currently at 15 miles. After explaining to them that the area they were in was a known GPS Jamming area (Bulgaria/Romania/Serbia). Captain did not believe this was the case and continued his explanation to why he thinks it wasn't jamming and it was indeed the GPS unit going out. Even though I told him that this same flight a week ago had GPS jamming happen in the same area. I got aircraft tech involved and they stated they couldn't find anything wrong with the GPS. After hearing this the Captain still wasn't convinced that it was GPS jamming and kept insisting it was a faulty GPS unit. He then proceeded to say he couldn't [fly] the Atlantic crossing with an ANP value of 15 and one GPS unit down. I assured him he could as I was reading from the circle of entry chart. I told him all that is needed since he was on random route was VHF VOR DME ADF and Mode C. He didn't believe me and instructed me to do my research and get back to him before he started the crossing which was over 2 hours away. He was adamant that if I couldn't provide him with sufficient info on why he can still do the crossing he was going to divert to ZZZZ. At this point my relief stepped in and I briefed him on the situation. He said he would research with help from Person A.Cause - Crew refusing to listen to Dispatch and not believing Dispatch that they were in a known area for GPS jamming. Train crews into knowing the signs of GPS jamming and the areas that it happens frequently in.