CME Group Inc. has again raised its bid for fellow broker-dealer GFI Group Inc., now offering $5.85 a share in cash and stock, as it tries to win over shareholders ahead of this month's vote.

CME and rival BGC Partners Inc. have been locked in a bidding war over GFI since last July. Brokers such as CME, BGC and GFI act as middlemen for Wall Street's big banks.

GFI has supported the efforts of CME. But BGC, the second-largest broker by market capitalization, went public with its intention to launch a tender offer for the company in September, after taking a 13.5% stake in GFI.

If the raised offer is approved at the Jan. 27 meeting, GFI management and certain affiliates will forgo about $40 million in consideration.

GFI rejected the BGC bid in November, calling it "highly conditional" due to an impasse over issues such as board seats. At that time, the board members suggested going ahead with CME instead.

CME originally offered $4.55 in cash-and-stock in July, and both parties have raised their bids multiple times.

Under the CME deal, CME would keep GFI's energy-trading platform, Trayport, and its pricing-and-data business, known as Fenics, and sell the firm's brokerage-and-clearing operation back to GFI executives.

GFI shares rose about 4% to $5.80 in premarket trading.

Write to Angela Chen at angela.chen@dowjones.com

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