The England international has won a host of domestic trophies at City since arriving in 2010 but the Premier League champions are yet to threaten in Europe.
Under Manuel Pellegrini, City made it out of the group stage of the Champions League for the first time last season before bowing out on aggregate 4-1 to Barcelona in the round of 16.
With City opening their season in the Community Shield against Arsenal on Sunday, Milner is eager for an impressive showing in Europe this season.
"Going further in the Champions League is definitely one of the major targets for the season," the 28-year-old told City's official website.
"Every team in the competition is in there for a reason - because they're the best in the continent - and we want to be right in there challenging for the trophy.
"It's never easy to get out of the group, as we've found out before, but hopefully our experiences in the last three seasons will aid us in our ambitions.
"The more experience we get in the competition, the better. Progressing from the group last year was great and will help us in our campaign this time around."
Milner is also predicting a difficult encounter against Arsenal at Wembley, with both sides bolstering their squads over the close season.
Alexis Sanchez was Arsenal's main arrival while City have brought in Bacary Sagna from the Emirates Stadium as well as Fernando and Willy Caballero.
"Arsenal are a really good team and always gives us a tough match," Milner added.
"I think they will be challenging for the title this year – they've made some good additions.
"They've strengthened but then, so have we – we've got some really good new players coming into the fold."
