Kim, who signed a two-year, $7 million contract this winter, started his Grapefruit League campaign 0-for-23 and is batting .182 in 48 Grapefruit League appearances.
Initially projected to be the O's Opening Day left fielder, Kim would have to agree to a move back to South Korea, which would be similar to what the organization did with right-handed pitcher Suk-min Yoon in 2014.
Rule 5 Draft pick Joey Rickard has been impressive this spring, prompting debate on whether he should get the starting nod over Kim, though Grapefruit League stats can be deceptive.
Additionally, Orioles reliever Dale Thayer opted out of his contact on Saturday.