Whelan wants to devote more time to chairing his home-town football club Wigan Athletic, which was promoted to the Premiership last season and faces champions Chelsea in its first top-flight match in August.
KPMG Corporate Finance chairman David Beever and Roger Lane-Smith, a senior partner at solicitor DLA, have been touted as possible successors.
Whelan is likely to retain a board position at the business he founded in 1976 and is reported to be keen to retain his 39 per cent stake in the company.
Any new appointment will come at a crucial time, with JJB facing stiff competition on the high street. Whelan, a former professional footballer, also faces challenges in his new field, with local police threatening to jeopardise the season's curtain raiser in a long-running dispute over unpaid policing bills.