The rapid loss of Arctic Sea Ice (ASI) in the last decades is one of the most evident manifestations of anthropogenic climate change. A transition to an ice-free Arctic during summer would impact climate and ecosystems, both regionally and globally. The identification of Early-Warning Signals (EWSs) for the loss of the summer ASI could provide important insights into the state of the Arctic region. We collect and analyze CMIP6 model runs that reach ASI-free conditions (area below 10^6 km^2) in September. Despite the high inter-model spread, with the range for the date of an ice-free summer spanning around 100 years, the evolution of the summer ASI area right before reaching ice-free conditions is strikingly similar across the CMIP6 models. When looking for EWSs for summer ASI loss, we observe a significant increase in the variance of the ASI area before reaching ice-free conditions. This behavior is detected in the majority of the models, and also averaged over the ensemble. We find no increase in the 1-year-lag autocorrelation in model data, possibly due to the multiscale characteristics of climate variability, which can mask changes in serial correlations. However, in the satellite-inferred observations, increases in both variance and 1-year-lag autocorrelation have recently been revealed.