Sprint Corp has agreed to pay about $40 per share to buy T-Mobile US Inc, a person familiar with the matter said, marking further progress in the attempt to merge the third- and fourth-biggest US mobile network operators.

The $40 price represents a 17 percent premium to T-Mobile US's closing share price on Wednesday, giving it a valuation of more than $32 billion and the shares have more than doubled in price since the group bought smaller rival MetroPCS a year ago.

Deutsche Telekom shares went up 0.24 percent to close at 12.44 euros on Thursday, valuing the German firm at over 55 billion euros ($76 billion).

However, Hannes Wittig, an analyst at JP Morgan, said the $40 price, if confirmed, seemed low.

"T-Mobile US should be worth more than that given that the synergies should exceed $20 billion, Deutsche Telekom would share some of the execution risk and Sprint would be getting control ... Somewhere in the high 40s would be more appropriate," he said.

Japan's Softbank, which owns Sprint, and Deutsche Telekom, which owns 67 percent of T-Mobile, still have to negotiate the details, including financing and the termination fee to be paid should the merger get blocked by regulators, the source said.

Analysts see the regulatory challenge as the biggest hurdle facing the companies since both the US Federal Communications Commission and Department of Justice have expressed a desire to have at least two more network operators competing against the market leaders AT&T and Verizon.

Under the proposed sale to Sprint Deutsche Telekom is expected to keep a 15 to 20 percent stake in the combined company, the source said.

It also remains to be seen what the break-up fee would be if the deal fails to gain regulatory clearance. Bloomberg said Softbank was pushing for a termination fee of $1 billion, while Deutsche Telekom wanted more like $3 billion.