With Nick Pope available again after injury and looking to reclaim his position as the first-choice goalkeeper, Dyche admitted he was in no position to keep all three happy.
"No, I can't see that position. There will definitely be one of them over time not so happy," Dyche told reporters.
"With players, the first port of call is to get the shirt and play. The second one is to be involved and then there's being out of the squad, and I don't think any pro wants that last one."
With three fit goalkeepers vying for one spot and seeking playing time in a bid to get an England call-up, Dyche expects departures at the end of the season.
"That's the way it goes and, come the summer, there will probably be a period where that works itself out," he added.
Burnley's next fixture is at Manchester City in a fourth round FA Cup clash and they return to league action on Tuesday at Manchester United.
(Reporting by Rohith Nair in Bengaluru; Editing by Amlan Chakraborty)
