The 26-year-old striker was heavily linked with a move away from the Merseyside club over the summer, after a disappointing season left them well adrift of Champions League qualification.
However, although a switch to Real Madrid looked to be on the cards, the Reds held firm to keep their man.
The decision appears to have been the right one so far, with Suarez having netted 17 goals in 11 league games to help Liverpool move into second place, and just two points behind leaders Arsenal.
Toure – a summer arrival – believes that his new side are in the race for the title, and that staying there can convince Suarez that they meet his level of ambition.
“Luis is here and we love him because he is a great player,” Toure told The Mirror.
“Of course we don’t want to lose him to another team. You can see that everyone from this team wants to improve the club and try to win a trophy.
“Luis said he wants to be part of a team that can win a trophy and I think now he can see that all the players want to fight and want to try to win this title definitely.
“We are challenging, every single game is really important for us and I think we started the game against Tottenham very well, very strong, and we played as a team.
“We fight, we attack, we defend together and that is very important when you want to challenge for the title.”
Suarez filled in as captain in the absence of Steven Gerrard during the weekend win over Tottenham, and netted two of the team’s five goals at White Hart Lane.