UPDATE 1-GE close to Avio deal for over 3 bln euros -sources

* GE could finalise deal for Italian company this week

* France's Safran still not out of race -sources

* Italy government regards asset as strategic

MILAN, Dec 17 (Reuters) - General Electric Co is close to finalising an agreement to buy Italian aerospace supplier Avio as early as this week for more than 3 billion euros ($3.95 billion), sources close to the deal said on Monday.

"Barring last-minute surprises, the deal could be closed between Tuesday and Wednesday, with an announcement on Thursday," said one of the sources.

A second source said the price is "more than 3 billion euros" and GE is the preferred bidder.

"Nothing is closed but there is a desire to get it done before the (Christmas and New Year) holidays," a third source close to the matter said.

Avio is owned by BCV Investments, in which Cinven private equity has a majority. Cinven bought the company in 2006 in a deal that valued the company at about 2.6 billion euros.

Avio was not immediately available for comment, while Cinven and General Electric declined to comment.

Another source with knowledge of the situation said a Thursday deadline sounded realistic since GE had been conducting due diligence for some time.

But the source added that France's Safran SA had still not given up on the deal and was trying to climb back into the race.

"I am not aware Safran is out of the race," a fifth source said.

Avio, which supplies engine parts for the Eurofighter Typhoon and engine makers GE and Rolls Royce Holdings Plc , has previously been in talks with other potential bidders including Safran.

The Italian government regards Avio as a strategic asset and is thought to be reluctant to let it fall into foreign hands.

Italian Prime Minister Mario Monti has already said he will resign once Italy passes the next budget law, and new elections are expected in February.

Italian defense group Finmeccanica, which owns around 14 percent of Avio, was in talks to sell a stake to state-controlled investment fund Fondo Strategico Italiano.

Finmeccanica is in a race to make 1 billion euros of asset disposals to help cut debt and avoid a credit rating downgrade.

Avio is a major supplier of parts for GE aircraft and helicopter engines, demand for which is expected to grow as Airbus, Boeing Co and other manufacturers whittle down record order backlogs.