MacKenzie, chairman and chief executive of The Wireless Group, attempted a management buyout to take the company private two weeks ago.
However, US media investment specialist Veronis Suhler Stevenson, which was backing MacKenzie, pulled out of the deal last week leaving Goldman Sachs with no choice but to send out a sale memorandum.
MacKenzie is believed to be lining up another private equity backer.
News Corporation, which owns 30% of TWG, has indicated it is open to offers for the £100m radio business.
The Wireless Group owns national station TalkSPORT, as well as 16 local radio stations. After winning the Edinburgh FM licence in December, it is due to begin broadcasting there later this year and has also submitted a bid for the Manchester FM licence.
News of the deal comes just after it was revealed that Scottish Media Group has rejected a £100m bid for Virgin Radio from Lord Waheed Alli, who was backed by private equity firm 3i.
Investors are waiting to see if Chrysalis, which recently bid £100m for Guardian Media Group's radio assets, will return with an improved offer.
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