In this letter, we investigate the impact of channel memory on the average age of information (AoI) for networks with various packet arrival models under first-come-first-served (FCFS) and preemptive last-generated-first-served (pLGFS) policies over Gilbert-Elliott (GE) erasure channel. For networks with Bernoulli arrival model, we first derive the average AoI under the pLGFS queuing policy, and then characterize the AoI gap between the FCFS and pLGFS policies. For networks with Bernoulli arrival and generate-at-will arrival models, the AoI performances under the FCFS and pLGFS policies are derived explicitly. For networks with periodic arrival model, we derive the closed-form expression for the average AoI under pLGFS over a general GE channel and propose a numerical algorithm for calculating that under FCFS efficiently. It is revealed that for pLGFS policy, the average AoI increases monotonically with channel memory $η$ at $\fracη{1-η}$ over the symmetric GE channel. For FCFS, the average AoI increases even faster due to the queuing delay, with an additional term related to the packet arrival rate.