Various applications for inter-machine communications are on the rise. Whether it is for autonomous driving vehicles or the internet of everything, machines are more connected than ever to improve their performance in fulfilling a given task. While in traditional communications the goal has often been to reconstruct the underlying message, under the emerging task-oriented paradigm, the goal of communication is to enable the receiving end to make more informed decisions or more precise estimates/computations. Motivated by these recent developments, in this paper, we perform an indirect design of the communications in a multi-agent system (MAS) in which agents cooperate to maximize the averaged sum of discounted one-stage rewards of a collaborative task. Due to the bit-budgeted communications between the agents, each agent should efficiently represent its local observation and communicate an abstracted version of the observations to improve the collaborative task performance. We first show that this problem can be approximated as a form of data-quantization problem which we call task-oriented data compression (TODC). We then introduce the state-aggregation for information compression algorithm (SAIC) to solve the formulated TODC problem. It is shown that SAIC is able to achieve near-optimal performance in terms of the achieved sum of discounted rewards. The proposed algorithm is applied to a geometric consensus problem and its performance is compared with several benchmarks. Numerical experiments confirm the promise of this indirect design approach for task-oriented multi-agent communications.