Sturridge has already scored against United this season, netting in Chelsea’s 5-4 Capital One Cup win at Stamford Bridge in October.
Rodgers suggested last week that Sturridge, who began his career at Manchester City, was now on his last opportunity to succeed at an elite club following his £12million move to Anfield.
And the forward said: “It’s amazing for the manager to put such faith in me. The only way I can repay him is by doing a job on the football field.
“For him to pay money for me and to have faith in me and show everybody around the world that he is prepared to take a chance on me, I don’t think I’ll ever be able to repay him for that.
“As a young player, when you play for big clubs you can sometimes get caught up in it and you never get another opportunity to play for a big club.
“So I’m grateful the manager has given me this chance and that he believes in me. I’m just glad to be here, really.”
Sturridge also had a slight dig at both United and former club Chelsea by adding: “In the Premier League, there is no bigger club than Liverpool.
“It is the biggest club I have played for. I thank the boss for giving me an opportunity to play for a club like this and I thank God for making it happen.”