According to a report in The Wall Street Journal Europe, the group of private equity firms is said to include Kohlberg Kravis Roberts & Co and Blackston, which are interested in buying the firm for around $7.9bn (£4.4bn).
The paper said an approach had already been made in March, but this was unsuccessful.
Shares in VNU were up 3.2% at €26.88 this morning as speculation broke.
This latest speculation comes at a crucial time for VNU, which is facing shareholder opposition to a proposed $6.7m deal to buy US healthcare data firm IMS Health.
Shareholders are concerned about details about how IMS will be integrated but, according to Reuters analysts, believe this latest private equity firm bid could help push through the deal.
VNU's brands include data firm AC Nielsen and magazines including Personal Computer World and Computer Active.
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