Cole has not featured for the Reds after aggravating a hamstring injury against West Brom on the first day of the season, with Lucas tearing a thigh muscle in the opening stages of the 2-2 draw against Manchester City at the end of August.
Rodgers told the club’s official website: "Joe is back in training with the group. He's still going to need a wee bit of time before he's anywhere near a game.
"He's been out for a few weeks now, so he needs a few weeks' training and a game or two below his belt before we can even consider him for the first team because he's broken down twice now and we need to manage that along."
Lucas is not expected to return until next month at the earliest, but Rodgers is positive about the progression of the Brazilian’s recovery.
He said: "Lucas is doing very well. He's working every day, working hard with the medical team."
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