Mulgrew, who helped clinch the Scottish Premier League title for the Bhoys this season, and Davis, who received the annual accolade in 2010, are joined by Dundee United skipper and joint-top scorer Jon Daly as well as Kilmarnock frontman Dean Shiels.
Davis 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.
"I am very proud to be captain of Rangers Football Club and I share this nomination with my teammates and the supporters who have backed the team in huge numbers during these difficult times."
PFA Scotland chief executive Fraser Wishart stated: "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."
Celtic left-back Emilio Izaguirre picked up the award last year.