Ireland wing Fitzgerald, who also featured for the Lions during the 2009 tour to South Africa , has been sidelined since May following neck surgery.
This caused the RaboDirect PRO12 Ambassador to miss last season's Heineken Cup triumph over Ulster and has kept him out of action for the Irish province throughout the 2012/13 campaign so far.
Centre Eoin O'Malley, who has also been sidelined all season, Dave Kearney (hip) and Shane Jennings (shoulder) are also in contention to return for the European champions, who suffered their third straight defeat at the hands of provincial rivals Ulster at the weekend.
Leinster have been ravaged with injuries so far this season, with Rob Kearney and Brian O'Driscoll having also missed large chunks of the season.
And Schmidt admits it will be the training sessions between now and the Connacht clash which will determine which of his players are fit to return.
"Hopefully we'll be in a position to welcome back Luke (Fitzgerald), Eoin (O'Malley), Dave ( Kearney) and Shane ( Jennings) either this week or next," Schmidt told TheScore.ie.
"It was also good to get Rob (Kearney ) and Brian (O'Driscoll) back on the field as they step up their respective programmes so.
"With a number of internationals set to be rested this weekend that presents some of the younger members of the panel with a further opportunity to gain experience that will hopefully add value to their development.
"We played well in parts of the Ulster game and it was frustrating not to get something for our efforts.
"But we also know that we've got to move on quickly and salvage as much as we can from the Christmas period."
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