The Welshman has not played a game since August 27, when he suffered a hamstring injury during the Reds' Capital One Cup defeat to Notts County.
"I'm almost there, basically," Allen told the club's official website. "The plan is to get back into training, get a good few days leading up to the Newcastle game and hopefully I'll be available for selection from there on.
"It has been a bit of a frustrating time, it always is when you're injured, but I'm finally getting there. It was the one I had in the back of my mind anyway, so it has worked out quite nicely in that sense."
Liverpool currently sit second in the Premier League table, level on points with Arsenal.