Chile's FIFA ranking of 73 was one of the reasons for the Department for Education and Employment preventing Gonzalez's summer switch to Liverpool.
Rafael is hoping to reapply for a work permit in January but, unless Chile rise into the top 70, there is a possibility they could be rejected again.
Chile need to beat Columbia on 8th October and Equador on 12th October to have any chance of playing in the World Cup finals in Germany.