Parse, who missed most of last season after undergoing hip surgery, suffered a lower-body injury Tuesday night against visiting Nashville, and coach Terry Murray said after the game he's "a little more than day to day."
Though he hasn't played since March 29 -- a 2-0 loss to the Kings in Edmonton -- Fraser has been a subplot since he was acquired from the Oilers last June in a trade that sent left wing Ryan Smyth back to Edmonton.
At the time of the deal, Fraser was known to have a foot injury that forced him to miss the last two weeks of the season. After the trade, the Kings claimed in a grievance filed with the NHL that the Oilers misrepresented the severity of the injury. The grievance has not been settled.
Fraser eventually underwent surgery in July to correct the injury, causing him to miss most of training camp. Fraser has been medically cleared and practicing with the team in a fourth-line role the last several weeks, however.
Fraser has spent parts of five seasons in the NHL, totaling 16 goals and 25 assists in 224 NHL games. He won the Stanley Cup with the Chicago Blackhawks in 2010.
Parse, 27, left Tuesday's game after taking three shifts in the first period and did not return. He has two goals in nine games this season.
Dan Arritt covers hockey for ESPNLosAngeles.com.