The brief is part of a strategy to drive consumers to the National Lottery's website.
Camelot will be looking to increase the popularity of its online games, with internet revenue currently only accounting for 4 per cent of its £90 million total weekly sales.
A number of agencies have been approached by Camelot to pitch for the project. It is not known if the incumbent, Hicklin Slade & Partners, which has held the direct marketing business for nearly nine years, will compete.
The news comes as both Camelot and the Indian lottery operator Sugal & Damani vie for the licence to operate the National Lottery as part of a statutory review.
Sugal & Damani, which has operated government-licensed lotteries in India for more than 30 years, has also kicked off a search for a direct agency to handle its below-the-line business.
The result of the statutory review is expected in August, and if Camelot is successful, the company will be taking on its third successive licence to manage the game since it launched in 1995.
Camelot is currently airing a campaign through its above-the-line agency, Abbott Mead Vickers BBDO.
The commercial backs its lotto product as well as driving customers to the website, which can be found at www.national-lottery.co.uk.