The striker has been running on the club's anti-gravity treadmill this week as he works his way back from a torn plantar fascia in his foot and Marsch expects Bamford back out on the grass next week.
Leeds have six games remaining in their Premier League relegation battle and Marsch believes Bamford, whose season has been ravaged by various injuries, will have a part to play.
"I do think it's feasible," said the American.
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"I think he's exactly on track for where we had hoped he would be. We're trying to be cautious and aggressive at the same time, and that's always the balancing act."
Bamford is an extreme example of the way injuries have made life difficult for Leeds in the top flight this season. The once-capped England forward has had an ankle problem, a hamstring issue, a quad injury and foot pain. Several players have suffered from hamstring injuries and key men have missed big chunks of the campaign.
Marsch credits the medical staff however for getting players back fit on schedule.
"I think one of the things that you have to give credit to with the medical team here is is there are statistics that have shown that we've had a lot of injuries over the past year, but that we get players to return quicker than a lot of places do and I think that's a credit to the medical staff and what they've been able to accomplish. So, for example, Junior Firpo came back much quicker than we had thought he would. So I would say that, Patrick, I'm cautiously optimistic that we can get him back and have him available for those last two matches like we hoped."
Marsch has Kalvin Phillips back at full fitness ahead of Monday's game at Crystal Palace, but Adam Forshaw is out for the season with a fractured kneecap.