PADUA, Italy, April 27 (Reuters) - Italian eyewear maker Safilo's (SFLG.MI) main shareholder is continuing talks with, mainly, four private equity funds and a deal is hoped for before end-June, chief executive Roberto Vedovotto said on Monday 27 April.

Safilo

Only 3T, which owns just over 39 percent of Safilo, last week confirmed the group was considering new funding to strengthen its capital base but said no concrete plans had as yet been made.

"We are continuing discussions. April 30 is not a deadline for the presentation of an offer," Vedovotto said after Safilo's annual shareholder meeting, referring to a date reported by a newspaper. "Due diligence should be finished soon. The hope is that the deal could be closed before the start of the summer."

It is the first time Safilo has said there are four private equity funds interested in the company even though "many more" have shown some form of interest, he said.

Vedovotto did not cite the names of the funds but said chairman Vittorio Tabacchi's family -- which controls Only 3T -- was talking "only to private equity funds which also have an industrial vocation".

Italy's La Repubblica newspaper said on Monday Apax, Bain Capital, CVC and PAI were in the running to take a stake and the deadline to submit bids was Thursday. It said details of the operation would be finalised by May 22.

CVC and Pai declined to comment, while Apax and Bain Capital were not immediately available to comment.

"It is a difficult process. Many actors are involved (and) the structure of the company is complicated," Vedovotto said.

Safilo shares were up 6.5 percent at 0.4450 euro at 1335 GMT.

Safilo, one of the world's biggest makers of glasses and sunglasses, is laying off workers and cutting production facilities, as the economic crisis hits demand. It had net debt of 570 million euros ($749 million) at the end of last year.

Vedovotto declined to comment on first-quarter trading.

During the shareholder meeting, Tabacchi said "up till now, it was reasonable to assume a particularly difficult first quarter. Improvements should be more evident in the second half of the year once (Safilo) starts to benefit from its industrial reorganisation plan". (Reporting by Cristina Carlevaro; Additional reporting by Simon Meads in London; Editing by Dan Lalor) ($1 = 0.7611 euro)