Streaming automatic speech recognition (ASR) hypothesizes words as soon as the input audio arrives, whereas non-streaming ASR can potentially wait for the completion of the entire utterance to hypothesize words. Streaming and non-streaming ASR systems have typically used different acoustic encoders. Recent work has attempted to unify them by either jointly training a fixed stack of streaming and non-streaming layers or using knowledge distillation during training to ensure consistency between the streaming and non-streaming predictions. We propose mixture model (MiMo) attention as a simpler and theoretically-motivated alternative that replaces only the attention mechanism, requires no change to the training loss, and allows greater flexibility of switching between streaming and non-streaming mode during inference. Our experiments on the public Librispeech data set and a few Indic language data sets show that MiMo attention endows a single ASR model with the ability to operate in both streaming and non-streaming modes without any overhead and without significant loss in accuracy compared to separately-trained streaming and non-streaming models.