The winning agency will be briefed initially with relaunching the company's Clinique for Men range.
The work will involve redesigning the brand's website and online advertising, as well as developing a strategy to target men more effectively.
The men's range of cosmetics falls within three main product categories: skincare, shaving and grooming. These include facial soaps and liquid face washes, a range of "Scruffing Lotions" of varying strength, an eye hydrator and lip balm.
The move follows last month's announcement by Estee Lauder that it had kick-started a review of its £200 million global media duties with a view to consolidating the brief into one network.
The company is considering three agencies for the pitch: WPP's Maxus, the US incumbent; Havas' MPG, a non-roster agency; and Omnicom's M2M, which handles the UK market for Estee Lauder.
In 2007, Estee Lauder's net sales exceeded £3.5 billion, up 9 per cent on 2006.