The sixth generation (6G) industrial Sub-networks (SNs) face several challenges in meeting extreme latency and reliability requirements in the order of 0.1-1 ms and 99.999 -to-99.99999 percentile, respectively. Interference management (IM) plays an integral role in addressing these requirements, especially in ultra-dense SN environments with rapidly varying interference induced by channel characteristics, mobility, and resource limitations. In general, IM can be achieved using resource allocation and \textit{accurate} Link adaptation (LA). In this work, we focus on the latter, where we first model interference at SN devices using the spatially consistent 3GPP channel model. Following this, we present a discrete-time dynamic state space model (DSSM) at a SN access point (AP), where interference power values (IPVs) are modeled as latent variables incorporating underlying modeling errors as well as transmission/protocol delays. Necessary approximations are then presented to simplify the DSSM and to efficiently employ the extended Kalman filter (EKF) for interference prediction. Unlike baseline methods, our proposed approach predicts IPVs solely based on the channel quality indicator (CQI) reports available at the SN AP at every transmission time interval (TTI). Numerical results demonstrate that our proposed approach clearly outperforms the conventional baseline. Furthermore, we also show that despite predicting with limited information, our proposed approach consistently achieves a comparable performance w.r.t the off-the-shelf supervised learning based baseline.