McDavid was announced as a Hart Memorial Trophy finalist for the 2018-19 season Sunday, Elliotte Friedman of Sportsnet reports.
McDavid has been named one of three finalists for the Ted Lindsay Award, reports TSN.ca. It is given to the most outstanding player as voted by his peers.
McDavid (knee) is expected to be ready for the start of the 2018-19 campaign, Darren Dreger of TSN reports.
McDavid will immediately begin rehabbing his leg injury, Jack Michaels of the Oilers Radio Network reports.
The Oilers don't believe McDavid's leg injury is serious, although they're still waiting for the results of an MRI, Jason Gregor of OilersNation.com reports.
McDavid notched a goal Saturday in a 4-3 overtime loss to Ottawa.
McDavid scored a goal and added an assist in a 4-1 win over Columbus on Thursday.
McDavid had two even-strength assists and four shots in Saturday's 3-2 loss versus Toronto.
McDavid chipped in a pair of assists in Monday's 4-3 win over the Sabres.
McDavid recorded three assists in Saturday's 4-0 win over the Blue Jackets.