Toure agreed a move to the Anfield outfit on a free transfer earlier in the window and he insists it would be a privilege to play alongside the Uruguayan.
Suarez has been at the centre of speculation all summer with Real Madrid considering a move while Arsenal are understood to have also joined the race to sign him.
However, the Ivory Coast international believes that Brendan Rodgers side are capable of going on to lift a trophy and feels the former Ajax man should reject any offers.
Toure said: "If he stays here, he can have more chances to win trophies.
"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."