Kidney Disease (KD) may hide complex causes and is associated with a tremendous socio-economic impact. Timely identification and management from the first level of medical care represent the most effective strategy to address the growing global burden sustainably. Clinical practice guidelines suggest utilizing estimated Glomerular Filtration Rate (eGFR) for routine evaluation within a screening purpose. Accordingly, the analysis of Electronic Health Records (EHRs) using Machine Learning techniques offers great opportunities to monitor and predict the eGFR trend over time. This paper aims to propose a novel Semi-Supervised Multi-Task Learning (SS-MTL) approach for predicting short-term KD evolution on multiple General Practitioners' EHR data. We demonstrated that the SS-MTL approach can (i) capture the eGFR temporal evolution by imposing a temporal relatedness between consecutive time windows and (ii) exploit useful information from unlabeled patients when labeled patients are less numerous with a gain of up to 4.1% in terms of Recall. This situation reflects the real-case scenario, where available labeled samples are limited, but those unlabeled much more abundant. The SS-MTL approach, also given the high level of interpretability, might be the ideal candidate in general practice to get integrated within a decision support system for KD screening purposes.