Blues boss Alex McLeish is hoping the on-loan Barcelona player will start to show his best form after "playing catch-up in terms of fitness" since arriving at St Andrew's.
Former Arsenal star Hleb was showing encouraging signs when he suffered the injury during the 1-1 draw at Fulham in late November.
McLeish said: "He is training well. The guys who are with him say he's been working very hard.
"He came to us half-fit from Barcelona. I don't think he had a full pre-season which is what you definitely need as a player.
"Sometimes you have got to build on a player's mentality and confidence as well as his fitness. Alex is playing catch-up in terms of fitness but we've been encouraged by the work he has put in this last week."