Content Delivery Networks (CDNs) distribute most data traffic nowadays by caching the contents in a network of servers to provide users with the requested objects, and helping to reduce latency when delivering contents to the user. The content caching system performance depends upon many factors such as where the objects should be stored, which object to store, and when to cache them. The proposed methodology includes two main phases: an admission control phase and a cache replacement phase. The admission control phase is responsible for accepting or rejecting the incoming request based on training the Reinforcement Learning (RL) algorithm to make the best decision in the near future to maximize its reward, which, in this case, is the hit ratio. The cache replacement phase estimates the object's future popularity. This is achieved by building a predictive model based on the popularity prediction mechanism, where the Long-Short-Term Memory (LSTM) model is used to compute the object's popularity. The LSTM model's outcome can help decide which objects to cache and which objects to evict from the cache. The proposed methodology is tested on a dataset to demonstrate its effectiveness in enhancing the hit ratio compared to conventional replacement policies such as First-in-First-Out (FIFO), Least Recently Used (LRU), Least Frequently Used (LFU) and a recent machine learning-based algorithm. The experimental results on the dataset revealed that the proposed methodology outperformed the baseline algorithms by 34.7% to 97.17% with a cache size of 130.