The problem of learning a communication policy is investigated in this paper for the design of an event-triggered observer for discrete-time LTI systems. Firstly, the event-triggered observer problem is formulated as an optimisation problem. The existence of a solution to this problem (communication policy) is investigated and it is verified if this solution still preserves the stability of the estimation error dynamics. Secondly, an algorithm is provided to approximate this optimal solution using neural networks and deep learning. Simulation examples are provided to illustrate the effectiveness of the learned communication policies.