* Rome warns Macquarie against all Enel's Open Fiber stake

* Italy must have control of Open Fiber if Enel exits

* Enel CEO Starace met Treasury officials on bid

ROME/MILAN, Sept 16 (Reuters) - Rome would welcome Macquarie buying a stake in Italy's Open Fiber as long as it fits with plans to form a national broadband champion, sources familiar with the matter said on Wednesday.

Macquarie Infrastructure and Real Assets has bid for all or part of utility Enel's 50% stake in Open Fiber, which is half-owned by state lender Cassa Depositi e Prestiti (CDP).

The government has told Macquarie it wants the fund to buy less than 50% so that CDP, which has a right of first refusal on any Enel stake sale, can take control, the sources said.

Enel and Macquarie declined to comment.

Italy is trying to broker a deal between Telecom Italia (TIM) and smaller rival Open Fiber to create a full-fibre network to close a digital divide with Europe.

Last month Rome set out a road map to try and overcome a deadlock between TIM and Open Fiber and create a high-speed network open to all operators and acceptable to regulators.

Under this plan, CDP would become an influential shareholder with vetting powers on strategic issues in the new player.

Macquarie, which in June made a non-binding offer valuing Open Fiber at almost 8 billion euros ($9.47 billion) including debt, presented a binding bid on Wednesday, the sources said, adding Enel's board would be informed at a meeting on Thursday.

Enel CEO Francesco Starace met Treasury officials to discuss the bid, one of the sources said.

The bid for a stake of 35-50% envisages several scenarios including possible political considerations, another added.

"There are earn-out clauses promising more cash if certain conditions are met," another source said, adding the deal could be worth anywhere up to the amount of the non-binding offer.

Vodafone and WindTre also have a right of first refusal on a combined stake of around 15% in Open Fiber in the event of ownership change. ($1 = 0.8450 euros) (Reporting by Giuseppe Fonte and Stephen Jewkes; Additional reporting by Elvira Pollina; Editing by Alexander Smith)