The government has not ruled out the option of completely separating BT from its infrastructure division Openreach, reports indicate.
Earlier this year, BT agreed to the watchdog's demand for its infrastructure subsidiary to become a distinct and legally separate company.
As part of this agreement, Openreach is required to offer its own distinctive branding, with any traces of BT's imagery removed to reflect its greater independence.
The deal with Ofcom also means that Openreach is being run by a newly-established board, the majority of which consists of directors independent of BT.
However, the Times is reporting that some government MPs still want to look at forcing BT to completely sell off Openreach.
A Whitehall official commented: "There are concerns that the market is just not competitive.
"Given what we’ve seen with BT’s current performance, we want the delivery of the next generation of broadband to be quicker and more competitive."