Gerrard has enjoyed a glittering 15-and-a-half year career at his boyhood club, winning every trophy possible aside from the top-flight crown.
But Liverpool are on course to end their 24-year wait for a 19th league title this season, with Brendan Rodgers' side top of the table with six games remaining.
And Sturridge, whose lethal partnership with Luis Suarez is a major reason behind Liverpool's success in 2013-14, has revealed the opportunity to add the one missing medal to Gerrard's collection is serving as an extra incentive in the Anfield dressing room as the campaign draws to a close.
"There's no-one more appropriate than Stevie to lift the trophy, not a chance," said Sturridge, who has netted 20 Premier League goals this term.
"If we win it, Stevie will really deserve it. He should win the Premier League because of everything he has done for this club.
"Every player in this team will do their best to help him achieve that goal."
England captain Gerrard's influence on Liverpool is showing no sign of abating despite his advancing years, with the 33-year-old having scored 11 top-flight goals this season - his best return since 2008-09, when the Merseysiders finished second.
And Sturridge insists the midfielder remains a key player for both club and country.
"He's just unbelievable every day, a great leader," added the former Chelsea man. "He lives and dies for this club.
"He's been here his whole career and it’s just a great pleasure to be able to play with him.
"He is the perfect example for every young player around the country, in fact a real example for every player. He’s been so loyal to Liverpool. He has been world class, and still is world class.
"Stevie will always be a legend not just for Liverpool, but to England as well. He will definitely go down in history as one of the best midfielders in the game, never mind just this club."
