They were nominated by their fellow professionals, whose votes will decide who succeeds Emilio Izaguirre.
Daly has scored 21 goals in all competitions this season and is challenging to be SPL top goalscorer. Shiels, who initially joined Killie on loan from Doncaster before extending his stay in January, has netted 11 goals in an advanced role this season.
Mulgrew has produced consistent displays in several positions and has netted seven goals while midfielder Davis, who won the title in 2010, has also found the net seven times.
In the Young Player of the Year category, Celtic winger James Forrest, St Mirren midfielder Kenny McLean and Dundee United pair Gary Mackay-Steven and Johnny Russell are all nominated for the award won by David Goodwillie in 2011.
The winners will be announced and presented with their awards at the Hilton hotel in Glasgow on May 6.
Davis, who could miss the rest of the season with a groin injury, said: "It is an honour and a privilege to be nominated again for the Player of the Year award and I would like to thank PFA Scotland and my fellow professionals for their votes."
PFA Scotland chief executive Fraser Wishart said: "This is the top award for players. There is no greater honour in football than to be voted the best player in your country by your fellow professionals."
The nominees in the First Division are Falkirk pair Farid El Alagui and Michael McGovern and Ross County's Michael Gardyne and Grant Munro. Ryan Donnelly (Airdrie), Steven Doris (Arbroath), John Robertson (Cowdenbeath) and Ryan Wallace (East Fife) are shortlisted in the Second Division.
Contesting the prize in the Third Division are James Longworth of Queens Park and Alloa contingent Kevin Cawley, Steven May and Ryan McCord.