Ibrahimovic is up for three end-of-season prizes following an impressive 22 goals and 10 assists in 27 matches for LA Galaxy since joining from Manchester United.
As well as the Landon Donovan MVP award, the 37-year-old has been shortlisted for the MLS Newcomer of the Year and MLS Comeback Player of the Year, despite his performances not being enough to earn the Galaxy a post-season place.
Former United captain Rooney, who moved to DC United from Everton in June, is up for the MVP and Newcomer prizes after inspiring his side to a play-off spot.
Atlanta United duo Miguel Almiron and Josef Martinez are also nominated for MVP, along with Los Angeles FC forward Carlos Vela.
The finalist for each award were voted for by MLS players, MLS club technical staffs and a select group of media representatives.