Britain's Daily Telegraph reported the 52-year-old was expected to be on the MCC shortlist of about six or seven candidates. There were initially more than 200 applications; interviews are expected at the end of the month, with the successful candidate likely to start before the next English cricket season.
The MCC are on the lookout for a replacement for Keith Bradshaw, who left his position as chief executive at the end of October, and the club have identified a playing background in professional cricket as a key requirement.
The Telegraph reported Snedden was on the shortlist with Steve Elworthy, the former South African bowler and current England and Wales Cricket Board marketing and communications manager, and Dave Richardson, the former South African cricketer and International Cricket Council (ICC) general manager.
Former Warwickshire batsman Wasim Khan, who has worked as chief executive of educational organisation Chance to Shine, is also thought to be a candidate as is John Stephenson, the MCC's head of cricket.
Snedden's reluctance to comment could be interpreted as interest. He is a straight-up individual and would have ruled it out if he wasn't keen on the job.
The MCC was founded in 1787 and is based at Lord's, widely regarded as the home of cricket. Once the world's most powerful cricketing body its influence has declined over time, especially after the ICC took over the running of the global game in 1993.
The MCC is still a prestigious organisation and has 23,000 members.