Phone company AT&T Wireless is studying bids for its business, believed to be from Vodafone and rival Cingular. The third-largest US wireless firm had set a deadline of 2200 GMT on Friday, 13 February, for offers to be lodged.
Cingular is said to have put forward a bid of about $35bn (�18.5bn), according to the Wall Street Journal.
Other reports had the UK's Vodafone submitting a bid of $34bn, but AT&T has refused to comment and will not make any announcement before Tuesday.
Deadline set
That is because Wall Street is closed on Monday for the Presidents' Day holiday.
AT&T has set itself a deadline of 29 February for naming the successful bidder.
Vodafone, the world's top wireless operator, and US rival Cingular appear to be in a head-to-head battle, although the New York Times named Nextel Communications as another potential bidder.
On Sunday, a Vodafone spokesman declined to comment on the reports or say whether the company had followed up interest expressed last week by submitting a formal bid.
A successful bid for AT&T Wireless would be Vodafone's biggest acquisition since it bought German rival Mannesmann for around �100bn in 1999.
Merged networks
Cingular, backed by parents BellSouth and SBC Communications, is viewed as the company with the most to gain in the bidding war.
It and AT&T Wireless operate their networks on the same technology.
By combining networks, the merged company could save $2 billion or more annually within a few years after an acquisition, analysts calculate.
AT&T shares rose 15 cents to $11.82 on the New York Stock Exchange on Friday and were the most heavily-traded stock.
Japanese newspapers said NTT DoCoMo, which already owns a 17% stake in AT&T Wireless, had decided not to participate in the auction.
Cingular had already submitted a $30bn (�18bn) informal offer for the wireless operator, but may have increased that by $5bn to trump Vodafone's bid.
Unexpected loss
For competition reasons Vodafone would have to ditch its 45% stake in US market leader Verizon Wireless if it did buy AT&T Wireless.
One option includes a swap, in which Verizon gives up its stake in the Italian operator Omnitel in exchange for a portion of Vodafone's ownership in Verizon Wireless.
AT&T Wireless announced in January that it would look at buyout offers after it posted an unexpected loss for the last three months of 2003.
The group blamed a host of technical and operational problems for its $84m (�50.5m) loss and announced its average revenue per customer had slipped to $58.70 (�35.30) - down 2.2% from a year earlier.