The 27-year-old joined the club on loan from Liverpool in January.
However, he has helped Palace win five games in those eight league games as the Eagles attempt to secure Premier League survival.
They are four points above the relegation zone with two games left and face third-bottom Hull on Sunday.
Sakho could miss the rest of the season though after suffering a knee injury in a defeat by Tottenham.
Palace have since also lost to Burnley and Manchester City.
Christian Benteke, Yohan Cabaye, Jason Puncheon, Andros Townsend and Wilfried Zaha are Palace's other player of the year contenders.
Crystal Palace have shortlisted Mamadou Sakho for their player of the season award despite making only eight appearances for them.