In a first-quarter update, he company said pre-tax profits had climbed to €1.78bn (£1.4bn) in the quarter, fuelled by a 7.2% increase in sales and a €517m gain from the sale of French cheese brand Boursin and the extension of its Lipton tea joint-venture with Pepsi.
The group said it was looking at the "best way to extract the best value" out of the world's market-leading olive oil brand.
Unilever would look to retain rights to Bertolli with any sale, as the company also sells a range of pasta sauces and snacks under the brand name.
The Bertolli business, which has annual sales of about €300m, was started by an Italian husband-and-wife team, Francesco and Caterina Bertolli, from a small shop beneath their home in the small Tuscan town of Lucca in 1865.
In the 1890s, the Bertolli's five sons, Giuseppe, Gioele, Giulio, Daniele and Elia, travelled abroad to the US, Australia, Brazil, Argentina and Africa, and started to spread the Bertolli name internationally.
The brand's possible departure from the Unilever stable comes two weeks after Brand Republic revealed Bartle Bogle Hegarty had resigned the £30m Bertolli European advertising account by mutual agreement following a seven-year relationship.
Bertolli is in the middle of a search for a new ad agency to handle the European account, which covers the UK, Germany, Belgium and the Netherlands.
The new agency will be required to create local adaptations of work produced by McCann Erickson New York, which has been working with the Bertolli brand since 2003.