The Reds unveiled Ivory Coast centre-back Toure and another new arrival, Belgium goalkeeper Simon Mignolet, at a Melwood press conference on Wednesday.
Toure, who has arrived from Manchester City on a free transfer, is hoping to get the chance to play alongside Liverpool's star player Suarez but accepts the Uruguayan's future is uncertain.
Suarez has been linked with a move to Real Madrid while top-four rivals Arsenal are also understood to have made an approach for him in the last week.
However, Toure believes there is no need for Suarez to leave and says the potential to land silverware is strong at Anfield.
"If he stays here, he can have more chances to win trophies," Toure told the media.
"This club is definitely prepared - the organisation, the mentality of players and staff.
"This is a top, professional club. It is amazing. He is a great player, a fantastic player. But it is up to the club to decide what they think will be best for everybody."
Toure, 32, says he is settling into life on Merseyside and has a good feeling, with just over a month to go before the new Premier League campaign kicks off.
"It's an honour to play for Liverpool. I have only been here for two weeks but I've seen a lot of good things," he added.
"This is a winning club and I want to be part of history here."