NEW YORK (Reuters)—Property and casualty insurer Alleghany Corp. is nearing a deal to buy Transatlantic Holdings Inc. for about $3.4 billion, a source familiar with the matter told Reuters, in the latest twist in a drawn-out battle for the reinsurer.

Alleghany is expected to pay $59 per share to $60 per share in cash and stock for Transatlantic, the source said, adding a deal could be announced as soon as Monday.

Shares of Transatlantic closed at $54.43 Friday on the New York Stock Exchange. Alleghany's expected offer price would mean a premium of about 8%-10% over Transatlantic's Friday close.

A deal with Alleghany could help Transatlantic ward off rival Validus Holdings Ltd., which has gone hostile in its attempt to buy the company.

Validus last offered to buy Transatlantic for around $55.35 per share and was also seeking to remove seven incumbent Transatlantic directors and have three of its nominees elected to the target company's board.

Transatlantic rejected Validus' offer as inadequate earlier this month and said it was continuing to pursue discussions about a potential sale to two other parties.

Those parties included former Berkshire Hathaway Inc. insurance executive Joseph Brandon, who at one point was working with Morgan Stanley on a possible bid for Transatlantic, and Enstar Group (ESGR.O), which has private equity firm J.C. Flowers as one of its largest shareholders.

Mr. Brandon is now working with Alleghany on the bid and is expected to join the company's management team, the source said.

Sough-after asset

Davis Selected Advisors, a key player in the success of any bid for Transatlantic as its largest shareholder, is supportive of the deal, the source said.

Alleghany, Transatlantic Holdings and Davis Selected Advisors could not immediately be reached for comment by Reuters outside regular U.S. business hours.

Transatlantic has become a sought-after asset as it is seen as relatively cheap and has 'long-tail' insurance lines, such as medical malpractice and worker compensation, that are attractive to reinsurers more exposed to 'short-tail' risks such as hurricane damage.

Transatlantic first struck a deal in June this year to merge with rival Allied World Assurance Co. Holdings Ltd., but had to call off that agreement in September after it became the subject of competing offers, including those from Validus and a unit of Warren Buffett's Berkshire Hathaway.

In September, the company also announced a $600 million share buyback program, aiming to repurchase $300 million worth of its shares by the end of this year.

Transatlantic was controlled by insurer American International Group Inc. until 2009, when AIG reduced its stake in an effort to raise capital following a U.S. government bailout.