We present preliminary ideas for a data-driven predictive control framework for linear quarter-plane causal (LQPC) 2D systems. These systems have doubly-indexed trajectories over $\mathbb{Z}^2$ and are governed by partial difference equations in two independent shift operators. Instead of identifying a Roesser or Fornasini-Marchesini (FM) model, we exploit the 2D Fundamental Lemma for LQPC input-output systems. It guarantees that every $N$-unfolding of every trajectory is parameterized by a single sufficiently informative data matrix, providing the two-dimensional analog of Willems` persistency-of-excitation condition. The classical model predictive control framework solves constrained quadratic programs with a moving horizon using an explicit mathematical model. Our approach retains many of the advantages of this framework, such as the receding-horizon structure, the enforcement of input-output constraints, and the feedback mechanism via boundary-condition updates. However, instead of using a model, we utilize a single informative input-output trajectory measured from the system. We parametrize admissible predictions through the basis matrix of system unfoldings. We provide some numerical examples to validate our proposed framework and suggest directions for future research.