Gerrard played in a strong line-up which beat Werder Bremen 3-2 in Switzerland on Tuesday evening in their first serious warm-up.
He insisted: "I've watched what the other teams are doing in the market and they're all strengthening.
"I'm not going to start making any unnecessary predictions about what's going to happen this season and the last thing any of us need to do is build hopes up too much.
"But without doubt, if we all perform to our level each week, we have the players to push United and Chelsea all the way.
"We are looking in great shape, not only going into this season but for the next few years.
"I thought going away for the summer that we were three or four players away from where we need to be.
"Now I think we are in a great place to challenge United and Chelsea and I hope if we get things right from the beginning we can beat them to the big prizes this year."