Babel was reportedly used as a makeweight for West Ham frontman Carlton Cole on transfer deadline day, however a deal failed to materialise.
And the Dutchman is determined to repay Hodgson by showcasing his talents to the Anfield faithful on a regular basis.
"It's clear when a new manager comes in, everyone's chances are equal again with others," Babel told the club's official website. "It is positive for me and maybe everybody who was in a difficult situation.
"I hope this is a chance for me to establish myself, but the first test for me is to work hard in every training session and try to show what I can do. In the end, it is the manager's decision if he uses me or not.
"I am very confident and positive - I feel well and have been training well. Hopefully it is just a matter of time before I can get some confidence back to finally show everybody what I can do."