Koskinen agreed to terms on a two-year contract with Swiss club HC Lugano on Monday.
Koskinen played 4:15 during Sunday's 4-1 win over the Flames in Game 3 while Mike Smith was being examined for a possible concussion.
Koskinen stopped 39 of 41 shots in Friday's 3-2 shootout win over the Canucks.
Koskinen will start Friday's season finale against Vancouver, Derek Van Diest of Postmedia reports.
Koskinen will defend the cage versus San Jose at home Thursday, Jason Gregor of OilersNation.com reports.
Koskinen gave up five goals on 23 shots in Tuesday's 5-1 loss to the Wild.
Koskinen is expected to start Tuesday in Minnesota, Mark Spector of Sportsnet.ca reports.
Koskinen will start against visiting Colorado on Saturday, Jack Michaels of the Oilers Radio Network reports.
Koskinen won't start Tuesday's game versus the Sharks, but he is clear of his illness and expected to back up Mike Smith, Jack Michaels of the Oilers Radio Network reports.
Koskinen (illness) will patrol the crease during Tuesday's road game versus the Sharks, source reports.