The new group would have a market capitalisation of £710m, with David Mansfield, chief executive of Capital, holding the same post in the new group.
It has also been agreed that Ralph Bernard of GWR would become chairman, in a deal structured as a nil-premium merger of equals. Cost savings would be substantial.
Analysts said merging the two would be the radio equivalent of the merger of Carlton and Granada to form ITV plc.
Both Capital and GWR declined to comment.
The Takeover Panel is likely to put pressure on the two radio groups to confirm the talks before the stock market opens for business tomorrow.
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Shares in both companies have risen in recent days on renewed speculation that the management teams and their respective advisers are back in detailed talks.
GWR’s share price closed on Friday at 262½p, giving it a market capitalisation of £343m. Capital’s share price closed at 430p, valuing it at £367m.
GWR has a collection of more than 30 local radio stations, which cover areas including Cambridge, Wyvern and Milton Keynes. They include Mercury FM, Coast FM and Buzz 97.1.
It also owns Classic FM, a national station that attracts a weekly audience of 7m listeners.
Capital runs London’s flagship commercial radio station, 95.8 Capital FM, as well as 19 other stations across the country.
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Gaining the support of Daily Mail & General Trust (DMGT), a 29.9% shareholder in GWR, will be crucial. DMGT said it was open-minded about a merger. In February, Capital reportedly made an approach to DMGT about acquiring the stake, but its offer was rejected.
Fidelity, the fund manager, is understood to be a keen supporter of the deal. It holds a 13% stake in Capital Radio and 9% in GWR. M&G, another fund group, is also a big investor in both companies.
Predictions of industry consolidation have been widespread following a change in the rules governing radio company mergers that came into effect recently.
The Communications Act allowed big newspaper groups to buy television stations. At the same time, the law was also changed to allow a single company to hold more than one national radio licence.
Nevertheless, the proposed deal would be looked at carefully by competition authorities: some estimate that Capital-GWR’s share of the radio advertising market would be 40%.