"Like ourselves, Chelsea will be upset at having lost out to United last season and I've no doubt they'll improve this time around," said the Reds' captain.
"Arsenal's young players will be more experienced and determined to make up for their disappointing campaign last time out and I also think a lot teams that finished outside of the top four have strengthened.
"So I definitely expect there to be more challengers for the title.
"It'd be stupid of me to make promises at this stage so I'm not going to say what we will or won't do in the coming season but we'll be giving it a right go, that's for sure.
"We're not too far away from where we want to be and with the new signings we've made this summer, plus the great players we've already got at the club, exciting times lie ahead at this club and it should be another exciting year.
"If I could pick one trophy for us to win it would be the League, if only for the fact that I'm being selfish and it's the one medal missing from my collection! But if we were to finish the season by winning JUST the European Cup - then you'll hear no complaints from me."