Cole has been a disappointment since signing from Chelsea on a free in the summer of 2010.
Form, fitness and injuries have all cast a shadow over his time on Merseyside and there are suggestions he could be moved on.
But the former England international capped a promising display against West Ham last week with a goal and Rodgers wants to see the 31-year-old kick on from here.
"Joe's game is very simple - it's about goals, assists, interceptions and tackles," Rodgers said.
"In the second half (against West Ham) he did all those things.
"When he gets the opportunity he has to take it. He's a good guy that works hard at his game."