He is believed to be in talks with JWT regarding a creative position at the agency. His partner, Jim Bolton, has also been linked to the move.
The news comes amid what sources close to HHCL describe as an unsettled mood at the agency after the decision last month by the chief executive, Nick Howarth, to join Clemmow Hornby Inge as its group chief executive.
Burley was promoted from creative partner to creative director in August 2003 to replace Al Young, who left to join FCB London as its creative director.
The move saw the agency split control of its accounts between him and the HHCL creative director and founding partner, Steve Henry, although Henry retained overall control of the creative department.
HHCL has previously had creative links with JWT, helping its sister agency with its winning pitch for the global HSBC business. However, any overtures by JWT for Burley's services are likely to draw down censure by WPP for infringement of its strict no-poaching rule.
Burley's departure, coupled with that of Howarth, is bad news for HHCL.
Both have played pivotal roles with the agency's key BSkyB client, which bills more than £60 million. HHCL's United network has also suffered key account losses, including Coca-Cola and Samsung, something that has thrown a question mark over whether its global chief, Andy Berlin, will seek to renew his contract with WPP when it expires next year.