David Moyes was announced as Alex Ferguson's successor in May and will officially start his new job on Monday.
And speaking to Sky Sports News, Gerrard says that all eyes will be on the new man.
Gerrard said: "They have replaced a world-class manager with another who has done a fantastic job at Everton, so I think David will continue to do a good job there.
"It is new for Manchester United. From a biased point of view, let's hope they have a wobble, but I think they have too many good players to fall out of the title race.
"They have world-class players and I expect them to fight for the league again."
Liverpool start their campaign with a home game against Stoke City while United travel to Wales to play Swansea City.