* Deutsche Boerse would be fined 10.5 mln euro under deal

* Deutsche Boerse: allegations "unfounded in all respects"

* Board to take some days to study settlement agreement (Adds statement from prosecutor, reporting credit)

FRANKFURT, July 18 (Reuters) - Deutsche Boerse said on Tuesday that Frankfurt's public prosecutor has offered to drop an investigation into Chief Executive Carsten Kengeter over allegations of insider trading if it accepts two fines totalling 10.5 million euros ($12.2 million).

Deutsche Boerse said that it was reviewing the matter, adding it "continues to believe the allegations made are unfounded in all respects".

Deutsche Boerse's board will spend some days reviewing the offer, outlined in a 10-page document that is not publicly available.

Acceptance of the offer would lift a cloud over Kengeter, whose reputation has been damaged by his failed attempt to merge with London Stock Exchange.

Shares in Deutsche Boerse were trading down 0.6 percent at 94.84 euros at 1511 GMT.

Earlier this year, as debate about the LSE merger was raging, police and prosecutors searched Kengeter's office and home amid concerns over Deutsche Boerse share purchases he made just months before the announcement of merger talks.

Kengeter has always denied the allegations, saying the purchases were part of an official Deutsche Boerse compensation plan.

"Insider trading goes against everything I stand for," he told shareholders in May.

One of the fines against Deutsche Boerse would be for the structure that the company had in place enabling Kengeter's share purchase.

The other fine would be for failing to publicly disclose the merger talks in a timely manner as dictated by German law.

"Deutsche Boerse has now been given the opportunity to respond," a spokesman for the public prosecutor's office said. He added that prosecutors had informed regulators about the status of the case. ($1 = 0.8642 euros) (Reporting by Tom Sims and Hans Seidenstuecker; Editing by Greg Mahlich)