The Brazil international arrived at the Yellow Submarine in 2009 for the sum of €16.5 million and has since scored only 26 goals in 85 matches in Primera Division.
Nilmar is reportedly among the top earners at El Madrigal at €95,000 per week, and following Villarreal's relegation to the Segunda it is believed that the club would like to cut their wage bill.
The Catalan giants are rumoured to be interested in acquiring the Brazilian, and it is speculated that the sum of €8m would be enough to persuade the Yellow Submarine to sell.
Nilmar's representative, Orlando da Hora, revealed that the player is on the wish list of former club Internacional, but stressed that there is interest from European clubs as well.
"There is a Spanish, one French, three Italian and one English team interested in Nilmar," said the agent as quoted by Marca.
Nilmar, who has a contract until 2014, has been struggling with injuries and poor form during his stint at Villarreal, and was thought to be close to leaving the club last year for Roma, but the Giallorossi's bid of €18m was declined.