The Reds are the only traditional 'big four' club not to win the English top-flight title since it became the Premier League in 1992, but the current campaign represents their best chance to break their duck.
Liverpool sit second, four points behind leaders Chelsea but with a game in hand, and are fresh off a 3-0 rout of Manchester United at Old Trafford - their fifth league win in succession.
Gerrard said Liverpool's revival this season from campaigns past should see former Swansea City boss Rodgers rewarded by the Anfield club.
"I am learning off him every day. When you become a more experienced player you look to see how the manager does - if he does the same things," Gerrard, 33, said.
"He has been fantastic for myself and I am sure the other players will echo what I am saying.
"We are absolutely delighted he is here and I just hope there is a lot of movement in Boston (owner John W Henry's home city) now as we speak because they have got to get him signed up as soon as possible.
"When players are in this situation with a year to go you want to keep hold of them so desperately, the club react really quickly and get it sorted, and for me I think he deserves a very long contract here and I think he is perfect for this club."
Rodgers, 41, was a relatively risky acquisition by Liverpool in 2012, but the Northern Irishman has vindicated the owners' decision so far, with Gerrard claiming his interpersonal skills are his greatest strength.
"He manages every single player. He knows we have different characters in the dressing room," Gerrard said.
"His one-on-one management is the best I have known. He makes you go out on to the pitch feeling a million dollars, full of confidence and belief.
"When you play for Liverpool you have to accept pressure, take it on the chin and perform, but when you have a manager who is making you feel good and who is not scared of giving you a good one-to-one telling off as well he has the perfect ingredients."
