The 31-year-old Argentina international has been sidelined since late February after breaking two bones in his back during the 4-2 Premier League win over Southampton.
In his absence, United have been eliminated from the Europa League and continue to struggle in the league, although they are six points clear of the relegation zone.
However, Coloccini is now back in training and could return to play a part in the season run-in.
"Colo is training," said Pardew. "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."
Coloccini is not the only injury Pardew has had to contend with of late with goalkeeper Tim Krul, full-back Davide Santon and midfielder Cheick Tiote all missing the weekend's game at West Brom.
In addition, Hatem Ben Arfa has only just returned to the first-team following a lengthy spell out and Ryan Taylor has missed most of this season and is likely to miss most of the next campaign with a serious knee injury.
However, Pardew is confident the injuries are the result of misfortune rather than anything the club is doing wrong.
"We have got a good medical team here," he added. "In all seasons, there are one or two [injuries] perhaps you could have prevented by holding them back, and maybe that's something we will look at."