New Liverpool midfielder
The 23-year-old's season-long loan move from Real Madrid was confirmed by the Reds on Saturday and he was in the stands at Anfield the next day to watch his new side draw 2-2 with league champion Manchester City.
With Liverpool putting in its most encouraging performance yet since
"If you watch the game against Manchester City, you see that the style the team is playing is very good and of course, Liverpool has to play in the Champions League," Sahin said.
"A big club like Liverpool has to play every year in the Champions League and we will do everything to get in the top four.
"Also there is the FA Cup, League Cup and Europa League, and with the potential we have here, we can do some good things."
Liverpool, which could only manage a disappointing eighth-placed finish last season, brought in Rodgers after he achieved success at Swansea City with a dynamic football philosophy.
It is a style of play the club's owners hope he can make work for the Reds and one Sahin believes he is well suited to.
"The project with Liverpool and
"I think the style I play is the same as how the manager wants the team to play.
"I have settled in very well and I hope it will be the same on the pitch and that we will have a great season."
Sahin was strongly linked with Arsenal before making the switch to Liverpool, but he is in no doubt that he has made the right decision.
"Everything people told me about Liverpool is there, what I see now," said Sahin, who has revealed Real's ex-Reds midfielder Xabi Alonso urged him to make the move.
"It is a very big club with a huge history and I think I have made the right choice."
Sahin joined Real last northern summer after catching the eye during a successful spell with German side Borussia Dortmund, with which he won the Bundesliga title in 2010-2011.
Once again he was a member of a championship-winning squad in 2011-2012 as Real claimed the Primera Division crown, but Sahin suffered with injuries and with there also being plenty of competition in midfield at the Spanish club, in the end, his involvement amounted to only a handful of first-team appearances.
This term, he is hoping to be far more a part of the action.
"This is very important for me after the injury I got last year," Sahin said.
"We became champions at Real Madrid, but I didn't play so many games, so for me it was important to come to a club where I had the chance to play at the highest level.
"I think in this case Liverpool is the best club for me right now."
Asked about the prospect of him making a permanent transfer to Anfield, Sahin said: "In football you never know.
"I am here for this season and then you never know what will be happening in a few months.
"I am looking forward to playing this year here and after, we will see."
Watford or Crystal Palace can still expect to receive £120 million ($204 million) if they are relegated from the English Premier League after just one year of top-flight football.