GMG already owns 18.5 per cent of jazz fm, which is based in London and Manchester, and has significant other broadcasting interests.
GMG chairman Paul Myners said: "Guardian Media will give the jazz fm business the economies of scale it needs to compete effectively as the UK radio industry is consolidating.
"This, together with Guardian Media's excellent track record of managing radio stations, will benefit the business and its employees."
GMG has offered 180p for each jazz fm share, a premium of 29 per cent over its closing price last Friday of 139.5p.
The bid has been accepted by Clear Channel International, which owns 30.9 per cent of jazz fm, and by Roger Parry, a Clear Channel executive director and jazz fm non-executive director, who holds 1.1 per cent. The offer is being considered by the jazz fm board.
New opportunities
The GMG board said there were "compelling reasons" for combining the businesses.
In a statement it said: "The radio industry in the UK has been consolidating in recent years, making it increasingly difficult for smaller radio groups such as jazz fm to compete effectively from a marketing and sales perspective.
"The board believes that the coming together of the parties' radio interests would generate a number of positive opportunities for jazz fm, including becoming a more attractive advertising medium to potential advertisers."
Guardian Media's radio division operates under the Real Radio brand and holds the regional licences for South Wales, central Scotland, South and West Yorkshire.
It also has a 39.2 per cent holding in Radio Investments, which operates 24 local radio stations, owns 33 per cent of the digital channel Oneword Radio, and has a 13.1 per cent stake in the MXR consortium, which holds regional, digital multiplex licences.
Jazz fm was launched in the London area in March 1990 and began broadcasting in the north west in September 1994. In the year to June 30, 2001, it turned over £8.01m and made profits of £134,000.
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