Brendan Shanahan was in Calgary on Friday to have dinner and a conversation with Flames president Ken King.
According to TSN Hockey Insider Bob McKenzie, no job offer was made but there was discussion.
Shanahan has been the National Hockey League's vice-president of hockey and business development since December, 2009 and became director of player safety in June, 2011.
There have been reports that the Flames may be looking to hire someone to head up their hockey operations.
Shanahan, 44, played for five clubs and won three Stanley Cup titles in 21 NHL seasons.