Rice, 27, is up there with the very best central midfielders on the planet and has proven his importance in the Arsenal squad this season as helps the side to fight for every competition available.
Manager Mikel Arteta has learnt to get the best out of him, but, many believe that his talent will be wasted if the England international does not start to collect trophies in what is the prime of his career.
Will Rice ever be compared to the Premier League greats?
Murphy believes that this is true and stated that he cannot be compared to some of the midfielders to ever grace the Premier League unless silverware is obtained.
"For Declan Rice to be spoken of in the same breath as a Gerrard or a Lampard, he needs to win the big ones, and he also needs to have the magic moments more often, like he did against Real Madrid," he said.
"When you think of Liverpool and Chelsea, and Lampard and Gerrard over the years, you can just pick moments - big games, big goals. Lampard against Barcelona. Cup finals. Gerrard in cup finals, European finals. The best players produce those magic moments to get the team over the line.”
Speaking more on what Rice needs to add to his game, Murphy stated that more goal contributions would raise his profile.
"I think he personally would want to contribute more goals and assists because he knows he’s capable," Murphy said.
"That’s one area of the game he’s really trying hard to improve, because we know technically he’s very good and when he gets in positions he can score, and he should be scoring more with the ability he’s got."