Gerrard is readying himself for his final Anfield appearance on Saturday evening, when the Reds play their last home game of his farewell season against Crystal Palace.
The 34-year-old will leave Liverpool at the end of the season to move to the MLS with the LA Galaxy.
Gerrard hopes Liverpool will be able to persuade young stars Raheem Sterling and Jordon Ibe to sign new deals, but he also feels adding quality from outside will help them challenge for major honours.
Liverpool find themselves outside the top four as the season winds down, having struggled for goals in the absence of Daniel Sturridge.
“There’s a core of players here with huge potential,” Gerrard said.
“I’m hoping the owners will back Brendan again, and bring in that bit of quality that help us go one step further next year.
“We’ve gone very close in a couple of cup competitions this year and we’ve also come close to the top four positions, and that’s with losing arguably the best player in the world last year in Luis Suarez.
“We’ve also not had our star striker available for most of the season in Daniel Sturridge, so to come so close without those two available… I think we’ve done okay but I think next year we can go one better.”
Watch Liverpool take on Crystal Palace on Saturday Night Football – coverage starts on Sky Sports 1 at 5:00pm.