The skipper sustained a grade two tear in his hamstring on international duty two weeks ago.
His recovery is going well and Liverpool's medical team is hoping for a return to full training early next week.
Dr Brukner told Liverpoolfc.tv: "Steven's going well. He's back running, though not back in training. He's certainly looking good to play the Newcastle game, which has been our target all along. We're hoping he'll be back in training at the start of next week. Everything's gone to plan."
Meanwhile, Joe Cole will travel to Bucharest with the team this week after recovering from a training knock which meant he couldn't face Tottenham on Sunday.
"Joe is in full training and is available for the Europa League game," said Dr Brukner. "He'll be travelling to Bucharest.
"He just had a minor injury in training on Saturday, which combined with the fact he was coming back after his hamstring problem meant we decided not to risk it. He'll be 100 per cent for Thursday night."
Meanwhile, Jamie Carragher's three-month spell on the sidelines will have Kopites hoping Daniel Agger soon returns to action after a lengthy calf injury.
Dr Brukner added: "He's starting to do some running. We expect him to be back in full training in a couple of weeks and available for selection before Christmas."