The consurtium has offered $27 per share, valuing the firm at $3.5bn (£2.2bn).
Focus Media, which is listed in the US, has been accused by research group Muddy Waters of overstating its assets.
The firm's shares have fallen more than 60% since hitting their peak in 2007.
It was also accused by Muddy Waters of overpaying for acquisitions.
Focus Media, which operates display advertising screens in offices and commercial spaces in China, has denied those allegations.
However, despite the firm's denial, its shares fell almost 40% on the day the allegations were levelled against it in November last year.
Though the stock has recovered since then, it is still trading at around $26 per share, well below the peak of around $66 per share in 2007.
Analysts said that the drop in share price had made the company an attractive buy for investors.
"We think the stock has been undervalued," said Jiong Shao an analyst with Macquarie Securities.
"Focus Media has a great business, generates tons of cash, pays dividend and buys back its shares."
Earlier this year, Focus Media reported a net profit of $37.9m for the April to March quarter, a 85% jump from a year earlier.
According to the firm, it has approximately 170,000 flat-panel displays in about 90,500 commercial buildings in over 90 cities in China.
The consortium behind the offer includes the Carlyle Group, CITIC Capital Partners and China Everbright Ltd.
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