T-Mobile is the fourth-largest mobile operator in the UK
Vodafone and O2 have both tabled bids of about £3.5bn to buy T-Mobile UK from owner Deutsche Telecom, the Sunday Times has reported.
The report says a decision was likely to be made within weeks.
A successful bid by either firm would make them the biggest mobile operator in the UK once T-Mobile's 16.6 million customers were added.
Vodafone and O2, which is owned by Spain's Telefonica, declined to comment on the report.
T-Mobile is currently the fourth-largest mobile operator in the UK, with a 15% share of the market.
O2 is the largest UK operator, with a 27% share, followed by Vodafone (25%) and Orange (22%).
France Telecom, which owns Orange UK, is also thought to be interested in T-Mobile.