The Reds are in eighth position in the Premier League after enduring a mixed start to the season under the Northern Irishman.
Liverpool were eliminated from the Capital One Cup by Swansea City but the Anfield side are set to face Zenit St Petersburg in the Europa League last 32.
Rodgers, who replaced Kenny Dalglish as Reds manager in May, is confident the Merseyside outfit can achieve their goals for the season.
“I love the expectancy and challenge of making this great club great again. I believe as we grow and work more together we will improve,” Rodgers told Liverpool’s website.
“This is a period of time where you have to keep your head down and work hard and give the players every chance to perform.
“The second half of the season, and in particular the last 10 games, I believe you are working to because that is the business end when things are decided.
“When you arrive at that period you want to get yourself in a good position to challenge, whether that is in the league or cup competitions.
“We can still achieve our objectives this season so when you can do that going into the second part of the season it gives you real hope.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news