Milner joined Liverpool from Manchester City on a free transfer in the summer.
Milner will face his old side Manchester City in the League Cup final at Wembley on Sunday as he has the opportunity to lift the first piece of silverware that's on offer this season.
In an interview with the Daily Mail, Milner said: "Liverpool has had such an amazing history but I would like to be a part of winning trophies here. I can see that happening.
"We don’t want to call this season a transition. We don’t want to say, “Never mind, let’s think about next year”.
"The league form has been erratic but we have shown at times it can be very good. At least we know we can get there and how good we can be."
The Reds certainly have the opportunity to win something to show for their efforts this season. As Milner has said, their league form has been erratic. They have put in some very good performances at times, and got good results, but there have been some games which have been at the opposite end of the spectrum.
They will be hoping for the kind of performance which recorded a 4-1 win over City earlier on in the season when the two meet at Wembley on Sunday, but before that is the important Europa League clash with Augsburg, with the two side's meeting at the last 32 stage of the competition following a 0-0 draw in Bavaria last week.
Given the club's current league position, the competition perhaps best represents Liverpool's best chance of qualifying for next season's Champions League, as well as being another opportunity for the side to win silverware.
Winning the next two games could keep the side on course for a season they could regard as a success, whereas defeats could see a dour end to the campaign.