According to senior sources at GMG as reported in The Times, the group values the stations at £150m to £175m and will not go below the asking price, making it highly unlikely the business will be sold soon.
Last month, GMG turned down the £115m offer from Chrysalis, which also owns the Galaxy FM regional stations. That bid was an improved offer on the £100m it had bid in January.
GMG, which also owns The Guardian and Observer newspapers, is in the process of rebranding Jazz FM as Smooth FM.
In addition to Jazz FM in London, GMG owns Smooth FM in the North West and Real Radio stations in South Wales, South and West Yorkshire and in Scotland.
GMG refused to comment on any bids it has received from Chrysalis, but GMG chairman John Myers told the Sunday Telegraph last month that the group had had a number of approaches "but none of these offers have reflected the true value we see in our radio portfolio".
The radio operations of the GMG are seen as a sideshow to its newspaper business, which also includes the Manchester Evening News. It could be set to add to that print portfolio with a London freesheet newspaper after it registered its interest in bidding for the upcoming London Underground distribution contract.
There has also been industry speculation that GMG chief executive Sir Robert Phillis may be close to retiring, because he has recently taken on non-executive roles at ITV and the Lawn Tennis Association.
If 59-year-old Phillis does retire in the next year it may result in a quicker sale because he was not as keen as Myers to sell the business.
In an increasingly consolidating radio industry, relatively small players like GMG may struggle to compete against giants like Emap and the soon-to-be finalised £625m merger of Capital and GWR's radio businesses.
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