This study addresses the challenge of real-time metaverse applications by proposing an in-network placement and task-offloading solution for delay-constrained computing tasks in next-generation networks. The metaverse, envisioned as a parallel virtual world, requires seamless real-time experiences across diverse applications. The study introduces a software-defined networking (SDN)-based architecture and employs graph neural network (GNN) techniques for intelligent and adaptive task allocation in in-network computing (INC). Considering time constraints and computing capabilities, the proposed model optimally decides whether to offload rendering tasks to INC nodes or edge server. Extensive experiments demonstrate the superior performance of the proposed GNN model, achieving 97% accuracy compared to 72% for multilayer perceptron (MLP) and 70% for decision trees (DTs). The study fills the research gap in in-network placement for real-time metaverse applications, offering insights into efficient rendering task handling.