Winner of the award in 2008/09, Cockerill is joined in the nominations by Lyn Jones of London Welsh, Dai Young of London Wasps and Mark McCall of Saracens.
The winner will be announced by Premiership Rugby at its awards ceremony at the London Hiton, Park Lane, on May 9.
"Aviva Premiership Rugby is fortunate to have some of the best coaches in the world working for our 12 clubs," said Phil Winstanley, the rugby director at Premiership Rugby.
"This is good news for the league but made the choice of selecting the shortlist very difficult and it is a credit to all four of these coaches that they made it on to the list.
The following awards will be made on May 9:
Aviva Premiership Rugby Player of the Season
Aviva Community Player of the Season
Land Rover Discovery of the Season
QBE Director of Rugby of the Season
Guinness Try of the Season
Gilbert Golden Boot
J.P. Morgan Premiership Rugby Sevens Player of the Season
Top Try Scorer of the Season
Gatorade Game Changer of the Season
The other shortlists will be announced over the next three days.
Director of Rugby of the Season: Previous Winners
2011/12 Rob Baxter (Exeter Chiefs)
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)