Birkenhead-born boss Nigel Adkins has steered the club to consecutive promotions with the help of Fazakerley native Ricki Lambert's goals.
Moyes said: "Southampton are a club who are doing very well. They have come up through a couple of divisions and are rightfully back in the Premier League.
"I am really happy with how we are playing but they will give us a hard game.
"They had a good win against Aston Villa last week and will probably feel more confident about where they are and I am sure they will come here and give us a decent game.
"Nigel Adkins deserves a lot of credit for his work. He has done great over the past few years and to get them up twice is a remarkable achievement."