The 50-year-old, who was confirmed as Sir Alex Ferguson’s successor in May, faces a tough opening five games as he aims to make a winning start to his Red Devils reign.
And Souness reckons Moyes will be desperate to beat Premier League title rivals Chelsea, who appointed José Mourinho as their new manager earlier this month, and make a big statement to the rest of the top flight.
“As a manager, when you get the fixtures, you want to win your first game and get off to a good start. But the second game they play, Chelsea at home, that’s the one he knows he must win,” Souness told Sky Sports News.
“If Moyes can put a marker down early against what will be one of his biggest rivals for the Premier League then he will have made a statement. But that will be a very hard game because Chelsea will be particularly strong next year.”
United won their 20th top-flight crown – 13th Premier League title – by a comfortable 11-point margin last season, with City finishing second and Chelsea further behind in third.