Conor O’Shea of Aviva Premiership Rugby leaders Harlequins and Exeter Chiefs boss Rob Baxter are the other men shortlisted by the panel of media professionals.
Cockerill previously won the award in 2008/09 in his first season in charge at Welford Road.
“The ebb and flow of the season has ensured it has been a compelling race for the Aviva Premiership title,” said Premiership Rugby chief executive Mark McCafferty.
“The undoubted strength of these three men reflects the size of the task for the panel and it looks like winning this award will be almost as hard as winning the Aviva Premiership Rugby title.”
The winner will be announced on May 8 at the sold-out Aviva Premiership Awards at The Hilton, Park Lane. The awards night will be shown on ESPN.
Previous Winners - Director of Rugby of the Season
2010/11 Jim Mallinder (Northampton Saints)
2009/10 Andy Key (Leeds Carnegie)
2008/09 Richard Cockerill (Leicester Tigers)
2007/08 Dean Ryan (Gloucester Rugby)
2006/07 Pat Howard (Leicester Tigers)
2005/06 Philippe Saint-Andre (Sale Sharks)
2004/05 John Wells (Leicester Tigers)
2003/04 John Connolly (Bath Rugby)
2002/03 Warren Gatland (London Wasps)
2001/02 Conor O'Shea & Brendan Venter (London Irish)
2000/01 Dean Richards (Leicester Tigers)
1999/2000 Andy Robinson (Bath Rugby)