The former Sun editor put the £100m company up for sale last week after a management buyout bid by him failed to win support.
News of the sale came after the radio group reported reduced financial losses down from £11.2m to £9.7m.
TWG is expected to be acquired by private equity groups, with 3i and CVC the most likely to be in the running with a serious offer by Friday's deadline. One trade buyer also believed to be bidding.
Initially, the radio company was attracting considerable interest from other radio operators, but this has since dried up.
Emap and Chrysalis have now decided not to bid because of the BBC's strength in sports broadcasting with BBC Radio Five Live.
It is expected that TWG, which owns national station TalkSPORT as well as 16 local radio stations, is unlikely to be sold for more than 90p a share, similar to a bid proposed by MacKenzie.
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