Bids were received yesterday from WPP, private equity firm Hellman & Friedman and French rival Havas.
WPP's offer was a cash-and-shares deal valued at more than $900 a share, or more than $1.25bn (£700m).
New York-based Hellman & Friedman, which is reported to have teamed up with buyout firm Kohlberg Kravis Roberts & Company, has also submitted a bid in the region of $900 a share.
However, there is no word on how much the bid submitted by Havas is worth.
The French firm's position is precarious. It needs the deal more than the other two, but it is bidding against the wishes of some of its most powerful shareholders, including Vincent Bollore.
Grey is expected to make a decision within the next few days but, according to sources quoted by the Financial Times, it does not appear that any bid was higher than Grey's current share price of $935.
Tim Fidler, director of research at Ariel Capital in Chicago, which controls 28% of Grey, told the paper that the bids "were not unreasonable", but fell short of his expectations.
He said the price had been kept down by the lack of competitors vying for Grey and the general state of the ad market.
"If it had been a more contested auction and a better advertising market, I think you would have seen higher bids.
"We are disappointed. It's a fantastic company. You don't want to see it monetised for the sake of cashing out," he said.
However, disappointed or not, the only opinion that counts in the race for Grey is that of Ed Meyer, the 77-year old chairman who controls the company.
There is no word on what Meyer thinks of the size of the bids, which at these prices it is estimated will net him a personal fortune of $34m.
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