Enrique has declared himself available for Liverpool's opening Barclays Premier League match against Southampton a week on Sunday.
The Spanish left-back made just nine appearances last season before undergoing knee surgery in November that brought his campaign to a premature end.
He resumed training in July and played in the Reds' pre-season tour in the US.
Jose Enrique: "I'm feeling good.
"I was training on my own and running a lot, and it's not the same when you play with a team because it's a lot more with the ball and a different type of running.
"I'm still getting my fitness back but I feel really good and confident that I can play soon.
"It's little by little, and not just me, everyone is getting their fitness. If the manager wants me to play in the first game of the season, I am ready of course.
"Liverpool has been for a while without Champions League.
"I've never played in the Champions League and I'm so excited to play in this competition because the best teams in the world are in this competition. I think Liverpool are one of the best teams in the world so Liverpool have to be there as well.
"We'll try to go as far as we can but of course not forget about the league and the two cups. We have a big squad and we want to compete for everything.
"Hopefully, like the manager says, we can win a trophy. We won one before with Kenny (Dalglish). I know it wasn't a Champions League or a league title but it was really exciting and for the fans it's really good to win trophies."