The Chicago-based buyout house has reportedly hired Bank of America Merrill Lynch to run the sale according to Reuters, which cited several people familiar with the matter.
That deal is expected to fetch less than $1bn, Reuters added, saying Apollo and THL had submitted first round bids this week.
GTCR bought into Capella, which operates more than a dozen hospitals across rural areas of the US, in 2005.
It has EBITDA of more than $100m, with GTCR hoping to collect almost 10-times that amount through the sale.
But the Reuters sources said there was currently a substantial price gap and that the deal may not go ahead.
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