The brand, which is marketed in the UK as Persil, has shortlisted Bartle Bogle Hegarty, Agency Republic and OgilvyOne to pitch for the global brief.
It is looking for an agency to create digital advertising to extend the "dirt is good" strategy online across ten markets, including the UK.
The selected agency will be expected to pay particular attention to the large Asian and South American online markets including India, Brazil and Argentina.
The "dirt is good" advertising strategy was created by Lowe before Unilever moved the lion's share of the global Omo advertising account into BBH in 2005. However, Lowe retained parts of the business in Asia, Africa and Latin America.
BBH works on the Persil account in the UK, and has recently released its second television ad for Persil's Small & Mighty liquid detergent sub-brand which launched last year.
The first commercial for the brand featured coloured clothes exploding out of a cap of Small & Mighty in the style of a fireworks display.
The second highlights the environmental benefits of the size of the product in the style of an animated children's pop-up book.
BBH won its first piece of Unilever digital business in January last year, when it picked up the pan-European Axe/Lynx business.
BBH's Lynx digital win was seen as evidence that traditional creative agencies are starting to match the specialists' offer when it comes to digital creativity.
Unilever had not returned calls as Campaign went to press.