You can use Alomafire itself do that:
NetworkManager
class NetworkManager {
//shared instance
static let shared = NetworkManager()
let reachabilityManager = Alamofire.NetworkReachabilityManager(host: "www.google.com")
func startNetworkReachabilityObserver() {
    reachabilityManager?.listener = { status in
        switch status {
            case .notReachable:
                print("The network is not reachable")
            case .unknown :
                print("It is unknown whether the network is reachable")
            case .reachable(.ethernetOrWiFi):
                print("The network is reachable over the WiFi connection")
            case .reachable(.wwan):
                print("The network is reachable over the WWAN connection")
            }
        }
        // start listening
        reachabilityManager?.startListening()
   }
}
Reachability Observer
@UIApplicationMain
class AppDelegate: UIResponder, UIApplicationDelegate {
func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey: Any]?) -> Bool {
        // add network reachability observer on app start
        NetworkManager.shared.startNetworkReachabilityObserver()
        return true
    }
}