This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and collaborates over a communication graph to reach exponential consensus on a consistent distributed approximation. The approach supports distributed computation under asynchronous and resource-constrained sensing. Its performance is demonstrated through simulation results, validating convergence and predictive accuracy under sensing-constrained scenarios and limited communication.