A deal could be finalised this week

Reuters has reported that the AT&T directors are mulling over the bids, which are both said to be $38bn.

However, the sale is being conducted in great secrecy, and AT&T, America's third largest mobile firm has yet to put out any statement.

In turn UK-based Vodafone has not yet confirmed that it is participating.

But investor fears about the possibility of it over-paying for AT&T have hit its shares, which closed down 2.57% on Monday.

AT&T Wireless has given itself until the end of this month to make a decision on the sale, but some analysts predict there could be a result as soon as Tuesday.

Ups and downs

Shares in AT&T Wireless, which has been a disappointing performer in recent years, have soared since the bidding began.

Vodafone needs a US acquisition, Mr Sarin says

Now, the market values the firm at just over $32.5bn, and a further jump is anticipated when trading resumes.

Investors in Vodafone, meanwhile, are less enthusiastic.

Many fear a return to the sort of lavish spending that characterised mobile-market strategy during the late 1990s - spending that now appears reckless.

Vodafone's chief executive, Arun Sarin, is relatively new and an unknown quantity in large international deal-making.

Jostling for position

Mr Sarin, meanwhile, argues that Vodafone needs a firmer foothold in the fragmented US market, where consolidation promises opportunities for acquisitive firms.

John Moroney of telecoms consultancy Octegra said buying AT&T Wireless could make sense for Vodafone provided the price was right.

"I think this is a good move for Vodafone in order to get its continuous branding across the globe," he told the BBC's World Business Report.

US-based Cingular, the second biggest US mobile phone network, is seen by some analysts as a closer fit for AT&T Wireless; aside from geographical factors, it and AT&T Wireless operate their networks on the same technology.

By combining networks, the merged company could save $2bn or more annually within a few years after an acquisition, analysts calculate.

Vodafone currently has a 45% stake in US mobile phone network market leader Verizon Wireless, but it is understood that it wants its own American network, carrying its own name.