The 31-year-old Argentina international has missed the last 11 games after breaking two bones in his back during the 4-2 Barclays Premier League victory over Southampton on February 24.
In his absence, the Magpies have slipped out of the Europa League and been sucked closer to the battle for top-flight survival, although they remain six points clear of the bottom three.
However, Coloccini's return to training means he could yet have a part to play, and that would come as a welcome boost to Pardew, who has found himself in the firing line as the fall-out from a disastrous derby defeat by Sunderland continues to shroud Tyneside.
He said: "Colo is training. He hasn't done full physical training - that's due to come, hopefully, this week.
"We are fingers crossed because obviously, that would be a big boost for us to have our captain back, for sure."