* Iliad in talks with partners possibly to improve its bid
* Sets limit on debt, capital increase used to finance bid
* Iliad offered $33 per share for 56.6 percent of T-Mobile US
* German parent company rebuffed that as too low (Adds detail on potential savings)
By Leila Abboud and Gwénaëlle Barzic
PARIS, Sept 1 (Reuters) - French low-cost telecom operator Iliad may improve its $15 billion offer for T-Mobile US but has set specific limits on how much money it would raise to fund any deal.
Iliad Chief Financial Officer Thomas Reynaud said on Monday that talks were continuing with private equity firms and companies interested in joining the group's pursuit of Deutsche Telekom's U.S. mobile business.
"The offer we made is still pertinent but it could evolve, not specifically in terms of valuation, but on the percent of the capital (that Iliad proposes to buy)," Reynaud said at a news conference after second-quarter results.
"To ensure that these discussions go to term, we cannot tell you more about them this morning."
Deutsche Telekom rejected Iliad's bid of $33 per share for 56.6 percent of T-Mobile US as too low in early August, but left the door open to an eventual U.S. exit.
The German company, which makes about a third of its sales and a fifth of core profits in the United States, has tried to sell T-Mobile twice since late 2011 because it sees it as too small to compete with market leaders Verizon and AT&T.
Deutsche Telekom spent about a year negotiating with third-placed Sprint over a potential sale, only to see it withdraw in early August over worries U.S. regulators would bar the deal on competition grounds.
Reynaud said Iliad would limit any capital increase to fund the T-Mobile bid to 2 billion euros. He also said Iliad's key leverage ratio would not surpass 4.5 times net debt to earnings before interest, tax, depreciation and amortisation (EBITDA).
Investors sent Iliad shares down 8.7 percent to 8-month lows of 152.65 euros at 1422 GMT because of concerns about its U.S. foray. The shares have fallen roughly 25 percent since July 30, the day before the announcement of its T-Mobile bid.
Stephane Beyazian, a Raymond James analyst with an "underperform" rating for Iliad, said the shares were falling because some investors believe the U.S. expansion is too risky, and would prefer Iliad to focus on consolidation in France.
"It's clear that Iliad prefers the U.S. option compared with going back to the table to negotiate to buy out Bouygues and consolidate France," Beyazian said.
Shares in French market leader Orange fell 3.3 percent on Monday, while third-place Bouygues Telecom fell 1.3 percent.
Iliad held informal talks with Bouygues about buying out the number three mobile operator earlier this year, but the two were far apart on price, sources have said.
A subsequent effort by Orange to engineer a joint bid for Bouygues with Iliad also fell through.
Iliad's Reynaud declined to say how long it would take to sign up partners for its T-Mobile bid, nor would he comment on when the group would submit a new offer to Deutsche Telekom.
Reynaud said Iliad had not yet won access to a so-called "data room", which is usually set up to give bidders access to information that is not public about a company it wants to buy.
Even without access to detailed information on T-Mobile, Iliad believes it can generate $2 billion in savings per year, or 7 percent of T-Mobile's estimated cost base, by running the operator in more cost efficient way.
That pledge has been met with scepticism by some analysts who say T-Mobile is already run in a quite lean manner. There has also been scepticism at Deutsche Telekom about estimates that the merger would result in $10 billion in benefits from cost cuts.
In a chart published Monday, Iliad said 38 percent of the $2 billion in cost savings would come from spending less on network, capex and equipment. A further 24 percent would come from information technology and general administrative costs, 20 percent from customer management, and 13 percent from marketing and advertising.
In France, Iliad has perfected a stripped-down way of operating, which has boosted its profitability, and it wants to export some of those practices, Reynaud explained.
"We know we can't just copy and paste Iliad's model in France to the U.S.," he said. "But there are some things that we do well, such as running call centres internally and boosting on-line sales that will translate to the new market." (Editing by David Clarke and Jane Merriman)