The Sunday Times reported that talks had concluded over the weekend and that a deal worth around £10bn will be announced early this week, with other reports suggesting the announcement will happen as early as Monday.
Both EE (owned by Orange and Deutsche Telekom) and O2 (owned by Spanish giant Telefonica) are said to be eager to secure the deal and both have been reported to be willing to accept a lower price including shares in BT as part of the deal.
On Thursday, Telefonica boss Cesar Alierta, flew into London to help get the deal finalised, but it remains unclear which mobile network BT has decided to acquire.
EE is the UK's largest mobile phone network with 28 million subscribers and it reported sales of £1.59bn for the last quarter. It was created in 2010 through a merger of Orange and T-Mobile in the UK and has positioned itself well in terms of 4G coverage, being the first UK operator to launch the next-generation network.
O2 has a 26.2% market share in the UK. If it was bought by BT, the telecoms giant would be re-acquiring the company, having spun off its BT Cellnet operation as O2 in 2001 and selling it to Telefonica in 2005 for £17.7bn.
BT is looking to offer quad-play packages to its customers (landline, mobile, TV and broadband) competing with Virgin and TalkTalk, while Sky is also looking to compete by getting into the mobile phone market as an mobile virtual network operator.