In her new role, Friedman will report to Nasdaq CEO Robert Greifeld.
Friedman joined Carlyle after leaving Nasdaq in 2011. According to the Wall Street Journal, she is now the leading candidate to succeed Greifeld.
In the meantime, Carlyle is reportedly close to exiting its investment in headphones maker and music streaming service Beats.
Apple is nearing a deal to buy the company, which was launched by legendary rapper Dr Dre and music mogul Jimmy Iovine in 2009, for $3.2bn.
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