Those challenging for the business are thought to include OMD and iProspect, whose sister Aegis agency Carat picked up the Wickes media planning and buying account at the end of last year.
The winning agency is expected to be appointed by the end of 2012.
Wickes appointed Carat to handle its £23 million media business in December 2011 after a final shoot-out against Walker Media. The previous incumbent, MEC, dropped out earlier in the process.
The retailer also appointed Partners Andrews Aldridge to its direct marketing account in February last year.
In September, Wickes introduced a brand character, called Wickesy the dog, in a social media and TV campaign for its paint range by the advertising agency MWO and the social media shop Jam.