The 39-year-old has endured a difficult start to his career at Anfield, with the Reds currently sitting 10th in the Premier League with just 28 points from 20 games.
However, the Northern Irishman has suggested that his players can still salvage their campaign if they give themselves a fighting chance over the coming months.
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"The second half of the season, particularly the last 10 games, you are working to because that is when things are decided.
"You want to get yourself in a position to challenge, whether in the league or cup. I believe we can still achieve our objectives this season."
Rodgers missed his side's last game against QPR at Loftus Road through illness, with the visitors cruising to a 3-0 victory.
The Merseyside club now have a chance to go eighth in the Premier League with a win against Sunderland at Anfield on Wednesday evening.