In several ASR use cases, training and adaptation of domain-specific LMs can only rely on a small amount of manually verified text transcriptions and sometimes a limited amount of in-domain speech. Training of LSTM LMs in such limited data scenarios can benefit from alternate uncertain ASR hypotheses, as observed in our recent work. In this paper, we propose a method to train Transformer LMs on ASR confusion networks. We evaluate whether these self-attention based LMs are better at exploiting alternate ASR hypotheses as compared to LSTM LMs. Evaluation results show that Transformer LMs achieve 3–6% relative reduction in perplexity on the AMI scenario meetings but perform similar to LSTM LMs on the smaller Verbmobil conversational corpus. Evaluation on ASR N-best rescoring shows that LSTM and Transformer LMs trained on ASR confusion networks do not bring significant WER reductions. However, a qualitative analysis reveals that they are better at predicting less frequent words.