The Scotsman started his second spell with West Ham around 18 months ago, with Noble happy to see him return.
"I got on so well with him the first time," Noble told the That Peter Crouch podcast.
"We had a great relationship and then I got a phone call saying the gaffer might be coming back and did I think it would be a good idea. I said 'yes' because I thought he was really good the first time.
"Don't get me wrong I was quite sad to see Manuel [Pellegrini] go as I got on well with him, we had some good times together but we just went on a bad run and I think that the Chairman decided to make the decision.
"The gaffer, Moyesy, rang me the day he got appointed and he asked me about the players, he knew a lot of them anyway and I think the players were pleased to work with him again, and the rest is history."