The Reds finished seventh in the Premier League last season in Brendan Rodgers' first term in charge at Anfield.
Rodgers has added four new faces in the shape of Simon Mignolet, Kolo Toure, Luis Alberto, and Iago Aspas to his squad this summer and he is still looking to bring in a couple more high-profile signings before the start of the new season.
Enrique believes with a few more additions Liverpool can challenge for success on all fronts.
"We already have a great team and we have more some new players and of course with more additions we can fight for everything," said Enrique.
"I think we have a very, very good team."
Meanwhile, Liverpool captain Steven Gerrard is happy with his fitness after making his first appearance of pre-season in Saturday's win over Indonesia All Stars.
Gerrard reported no ill-effects from his first action since undergoing shoulder surgery earlier this year and the midfielder is keen to get more action under his belt ahead of the new Premier League campaign.
"My shoulder felt fantastic, so it was nice to get the first 45 minutes under my belt and hopefully I'll get slightly more time in Australia.
"It's been feeling fine now for a few weeks in training, there have been absolutely no problems.
"The surgeon gave me the go-ahead to play and the manager was sensible in giving me 45 minutes. I'm really happy with how I feel.