Moyes' first home game in charge of United will be against Chelsea on August 24, and Souness says there will be a lot of pressure on the new Old Trafford boss to score a vital victory.
"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," former Liverpool boss 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."