Luis Suarez is currently the only recognised striker that Rodgers has at his disposal, after the Reds failed to sign a replacement for Andy Carroll in August and then lost Fabio Borini to a broken foot earlier this week.
"There are still areas we want to reinforce and we have to reinforce as soon as we can," Rodgers told the Daily Mail.
"Our best team are comparable to any team in the Premier League. But we're a very thin squad and we are having to challenge on a lot of fronts.
"I've had good conversations with the owners and they understand where we are at as a team."
Liverpool sit 14th in the Premier League table, having taken six points from their opening seven matches.