The biological carbon pump (BCP), involving photosynthesis at the surface and remineralisation at depth, maintains a significant vertical gradient in dissolved inorganic carbon (DIC), promoting the ocean's ability to absorb atmospheric CO<sub>2</sub>. Remineralised DIC is a good indicator of the strength of the BCP. It can be estimated from apparent oxygen utilisation (AOU) that measures the deficit of oxygen compared to saturation. AOU is projected to increase under climate change due to changes in remineralisation rates and circulation. However, the amplitude of the change is still uncertain. Here, we identify linear relationships between AOU trends and age trends in the deep ocean in simulations of the contemporary (1972–2013) and future (2015–2099) periods from five Earth system models (ESMs). Linear relationships identified within observational data for the contemporary period indicate that ESMs overestimate the sensitivity of AOU to age changes in the deep ocean. The study highlights the stability over time of the AOU sensitivity to age changes, suggesting an overestimation of the BCP strengthening inferred from AOU. Furthermore, our analysis underscores the substantial role of circulation slowdown in increasing remineralised DIC. These insights emphasise the challenges and opportunities to constrain future BCP projections due to circulation uncertainties.