The company is believed to be vying with Orange to sponsor the games, but has recently gained an edge over its rival and is now in exclusive talks with the 2012 organising committee, Locog.
The telecommunications deal is one of the most complicated sponsorship packages at the games, because it includes installing communications equipment at the venues in addition to a substantial cash fee.
In return, BT will have exclusive 2012 marketing rights in the UK, from use of the London Olympics logo to tickets and hospitality packages.
The company, which has now gained preferred bidder status, helped to fund the bid to host the 2012 games.
An announcement is not expected until April. BT said no decision had been made but confirmed it was "interested" in becoming an official sponsor.
The organising committee has already signed up Lloyds TSB, EDF Energy and Adidas as tier-one partners.
The committee was originally intent on securing all tier-one partnerships before shifting attention to its second-tier tie-ups.
However, Deloitte has already been named a professional services partner in the second-tier category.
Other vacant categories include: official airline, with British Airways understood to be in the running; and the clothing and homeware category, with Tesco and Sainsbury's reported to be battling it out to become official backers.