Billionaire Xavier Niel’s Iliad is talking to private-equity firms about teaming up to make an improved offer for Bellevue-based T-Mobile US, according to people familiar with the matter.

Iliad’s discussions with potential partners may accelerate after T-Mobile’s parent, Deutsche Telekom indicated it’s willing to talk if a bid puts a valuation of at least $35 a share on the business, said the people, who asked not to be identified because the talks are private.

The German company hasn’t received a new proposal, and there’s no guarantee a higher offer will be made, they said.

Financial and industrial partners have approached Iliad about a joint offer for T-Mobile, Chief Financial Officer Thomas Reynaud said at a news conference in Paris on Monday.

Iliad has been talking to U.S. buyout firms as well as companies and sovereign-wealth funds, the people said.

“Our offer is still valid, and probably even more relevant than at the end of July,” Reynaud said, calling a joint bid for a larger T-Mobile stake “one of the options.”

Iliad’s previous cash offer of $33 per share, or $15 billion, for a 56.6 percent stake in T-Mobile, was rejected as too low.

At a strategy meeting Thursday, Deutsche Telekom senior managers discussed $35 to $40 as a realistic per-share valuation range at which the carrier would be willing to begin negotiations, said a person familiar with the matter. Reynaud declined to say whether Iliad plans to increase its bid.

Deutsche Telekom’s valuation of T-Mobile opens the door for an improved bid from Iliad or new proposals from potential suitors such as Dish Network after Sprint last month withdrew from talks to buy the unit.

Iliad is aiming to replicate in the U.S. its French tactics of gaining market share with rock-bottom prices.

Iliad’s last proposal projected $10 billion in potential savings and gave an overall value for T-Mobile of $36.20 a share by including such synergies.

T-Mobile shares closed at $30.08 Friday, valuing the company at $24.3 billion.

Some Iliad shareholders are concerned about slowing growth in its French home market, Borrega said.

Deutsche Telekom, which owns about 67 percent of T-Mobile, would consider forgoing a higher price if that meant avoiding the uncertainty of a prolonged regulatory review, said people familiar with the matter last month.

The company wants to avoid reliving its failed attempt to sell T-Mobile to AT&T for $39 billion.

After that accord in 2011 was opposed by the U.S. Federal Communications Commission and the Department of Justice, T-Mobile proceeded to merge with MetroPCS Communications.