UPDATE 1-Ad agency Cossette mulls 4th Cosmos proposal

* Cosmos now says willing to pay C$8.10 a share

* Takeover battle has raged since July

* Cossette shares halted at C$8.01

By Pav Jordan

TORONTO, Nov 17 (Reuters) - Cosmos Capital has said it is willing to pay C$8.10 a share to buy Cossette Inc KOS.TO, but the advertising agency's board said on Friday it needs proof the private equity group can come up with the cash.

The offer, if made official, would raise the price tag on Quebec City-based Cossette for a fourth time since July and for the second time this week.

"Further information is required in order for the board to determine whether Cosmos' proposal at C$8.10 per share could reasonably lead to a superior proposal," Cossette said in a statement after the market closed.

Montreal-based Cosmos was not available for immediate comment to confirm the proposal, which would value Cossette at C$135.3 million ($126.4 million). That would be slightly higher than a rival bid by U.S. private equity group Mill Road Capital at C$7.87 a share, or C$131 million, which Cosmos also matched earlier this week.

A takeover battle has raged around Cossette since July, when Cosmos, whose investors include two founders of the ad agency, made a first bid at C$4.95 a share, which was rejected as too low.

Cossette is small by international standards -- ranked about 23rd globally -- but it is Canada's largest homegrown shop, expanding from a tiny company in the early 1970s to a transnational with Canadian clients like McDonald's, Bell Canada, General Motors and Coca-Cola.

Cossette's allure includes a strong presence in the French-speaking province of Quebec, a difficult market to crack for foreign companies. It also has assets or offices in the United Kingdom, where it set up in 2003, as well as in the United States and China.

"Cossette recommends that its shareholders defer making any decision until its board of directors has had an opportunity to fully review Cosmos' amended offer," the company said in a statement.

Cosmos, which is being advised by Genuity Capital Markets, controls 18.7 percent of Cossette. It also has lock-up agreements with Bergundy Asset Management, which holds 11.1 percent, and Beutel Goodman & Co, with 7.6 percent of the shares.

Cosmos said its offer earlier this week was fully financed, but it was conditional on due diligence and on receiving access to Cossette's virtual data room after it was barred from it in July, following its first hostile bid.

Cossette said on Friday that Cosmos made its C$8.10 per share offer in a letter to the special committee of the board, saying it was prepared to offer that price subject to the same due diligence conditions.

Cossette is being advised by BMO Capital Markets (BMO.TO). Its shares were halted on Friday at C$8.01.

($1=$1.07 Canadian)) (Reporting by Pav Jordan; editing by Rob Wilson)