Executives at Global, which is headed by former ITV boss Charles Allen, are adamant that they do not want to overpay for the UK's biggest commercial radio group.
The company has been given until this Wednesday to strike a deal with GCap, or refrain from lodging further bids for another six months.
But one analyst said that Global's latest offer of 202p a share, an increase of 12p on its original offer made in December, was deliberately under-priced. Paul Bates, an analyst at Charles Stanley, said: "202p was never going to be accepted and, therefore, was a kind of kite-flying exercise."
However, a source close to Global said it was "hard to see Global offering too much more".
With the clock ticking on Global's chances, the option of waiting six months, while monitoring stock market performance and GCap's share price, might seem attractive, according to some analysts.
"What's to stop it (Global) waiting for six months when the advertising market is at a lower point and GCap's share price has dropped?," asked one.
Global may now turn its attention to Scottish Media Group's Virgin Radio. UTV, radio consultancy Absolute Radio and Astro All Asia Networks are also potential bidders.
Global has already lost out in the race to acquire Emap Radio, and another failed acquisition could damage its credibility as it looks to establish itself as a major radio player.
"If it happens to them again, they won't look good," said Bates.
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