IDH, which serves NHS patients and operates private practices, could be valued at £1bn in a deal, said Sky.
Carlyle has asked investment banks to make pitches for a role on advising it on a deal later this year.
The chain said in bondholder filings for the last quarter of 2013 that its EBITDA for the fiscal year to date climbed 21 per cent to £48.7m, according to the report.
In the meantime, Carlyle is reportedly nearing a deal to sell its interest in Beats to Apple.
The headphones maker and music streaming service is expected to be valued at $3.2bn.
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