JP Morgan has been conducting a strategic review of the business, which is under the new management of Richard Moat, assessing the company's stand-alone options as well as the viability of a sale, banking sources also said.
A figure of 4bn has begun circulating in the media as a price Deutsche Telekom hopes the business would fetch.
T-Mobile UK began losing customers last year as it failed to keep up with new deals and handsets offered by rivals, raising expectations that it was ripe for a takeover.
Bernstein Research analyst Robin Bienenstock said all operators would benefit from a consolidation of the crowded UK market, where five companies compete, and that it would be better to be a buyer than a bystander.
"We estimate value creation for Vodafone and O2 to be 6 billion and for France Telecom about 5bn were they to purchase T-Mobile UK," he said in a research note, adding that France Telecom should be comfortable with paying just over 3bn. "This does not include T-Mobile UK tax assets which we believe to be worth about 2bn , he added.
Andrew Hogley, an analyst at Execution Ltd, said he valued T-Mobile UK at 4.2bn, adding that Deutsche Telekom would want to realise proceeds of over 5bn in any transaction.
Such a figure would be a tall order in the still fragile M&A market, where buyers of assets are in short supply despite the rallying markets and stronger economic outlook. While company bosses are more confident and deal pipelines are improving, buyers still tend to harbour radically lower ideas than vendors when it comes to talks over what an asset is worth.
Any would-be acquirer would also have to take into account the risk that a deal could be blocked by Britain's competition regulator, which said in July it was happy with the state of competition in the market.
O2 currently has about 27 per cent of the UK market, followed by Vodafone with 25 per cent, France Telecom's Orange with 22 per cent, T-Mobile with 15 percent and Hutchison Whampoa's 3 UK with 8 per cent.