The former Chelsea midfielder won three league titles at Stamford Bridge and he hopes his move to Anfield will continue his medal haul.
"The target of a club like this is the number one place," said Cole.
"There was a lot of difference last season but we are starting afresh and we will be doing everything we can.
"When you play for Chelsea it (winning the league) was expected every year.
"When you come here the whole place is willing it to happen. You can feel that energy and I just want to do my best for the club and if that means we can put some pots on the table then that will be great.
"You just look at the history of the place and it is great that I am pulling on the same shirt as people like Kenny Dalglish, John Barnes - great players.
"I am 28 now and coming into my peak years and I want to be at a club where I am on the pitch as much as possible and helping the team to really do something special.
"I need to feel my confidence again, get myself back to my best, but hopefully I can give my best years to this club.
"I wouldn't have come to the club if I didn't think we could do things and I just need time and games and we will all do it together."