The company's share price plunged 10 days ago after TNS issued a profits warning and said that turnover at its US division was declining.
Along with losing a major IBM account in 2005 and the increase of online market research competitors, there is increasing pressure on chairman Donald Brydon and chief executive David Lowden to improve the company's fortunes.
According to thisismoney.co.uk, TNS is reported to have received approaches from at least two private equity firms before its recent profits warning.
WPP, Aegis, Omnicom, Germany's Gfk and Ipsos of France are also among the list of likely bidders for the research giant.
Following the trading statement earlier this month, meetings between TNS' investors and management have been described as "disastrous". Sources say investors were keen to learn more about the problems in the US but TNS refused to comment.
Investors are said to regard Lowden, previously the company's chief operating officer, as "substantially responsible" for the troubles in the US market. Lowden himself admitted earlier this month that the performance of its US division was "unacceptable".
TNS, which operates in more than 70 countries, made £85m profit on turnover of £999m last year. When the FTSE closed on Friday, TNS's share price stood at 166.5p, but had recovered this morning to 173p.
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