The Uruguayan striker has been linked with a move away from Anfield throughout the summer, with Arsenal interested in signing him.
"We've got some wonderful youngsters who are growing each year," Gerrard told BT Sport.
"Hopefully we keep our magician (Suarez) number seven and we can have a crack at winning things this year. That's what I want to do in my final few years, just compete and challenge for top honours.
"It's not down to me [if Suarez stays] it's down to himself to make a huge decision. It's all about himself and his family, but the people at Liverpool, they absolutely adore him."
Liverpool beat Olympiacos 2-0 today in Gerrard's testimonial game.