A club official said Monday that nothing is "imminent" with the 40-year-old Seattle icon, who is among the plethora of hitters struggling at the plate this season, but the production of several players has been "disappointing."
The official would not comment on a Tacoma News Tribune story published Monday that said, "He could lose his job as the left-handed designated hitter within the week. He might lose his position on the 25-man roster nearly as soon."
Mariners manager Don Wakamatsu was en route to Baltimore and general manager Jack Zduriencik, who did not accompany the team to Baltimore, could not be reached for comment.
Calls placed to Griffey's Cincinnati-based agent, Brian Goldberg, also were not returned.
Griffey, who signed a one-year contract to play at least one more season with the Mariners after his celebrated return to the team in 2009, currently is batting .208 with no home runs and five RBIs.
According to the News Tribune story, which did not quote players by name, when Wakamatsu wanted to use Griffey as a pinch-hitter recently, the player was asleep in the clubhouse.
That could not be confirmed by MLB.com.
The Mariners were considered a potential playoff team at the beginning of the season, but an eight-game losing streak during the just-ended homestand left the team in last place in the American League West.
The offense has only one position player -- center fielder Franklin Gutierrez -- batting higher than his career average.
Griffey has not been as outgoing in the clubhouse as he was last season, but he said during Spring Training that if he were too upbeat when the team was struggling, it would be characterized as him not caring whether the team wins or loses.
The Mariners are scheduled to face right-handed starters throughout the road trip, which means the left-handed Griffey would normally start. The trip includes stops in St. Petersburg against the Rays and in Oakland before returning to Seattle to face the Blue Jays on May 19.
Jim Street is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.