The (Cleveland) Plain Dealer reported online a team source confirmed that the two players are facing academic issues but said no final decisions will be known until Wednesday.
Carter ranks third on the team in receiving yards (176) and tied for fifth in receptions (13). He appeared in all 12 regular-season games as a true freshman and served as the team's No. 4 wideout behind DeVier Posey, Dane Sanzenbacher and Ray Small.
Rose played in 11 games as a reserve for the Buckeyes, recording 10 tackles, three for loss, and two sacks.
A team spokeswoman couldn't confirm Tuesday that both Carter and Rose are out for the game. Ohio State faces Oregon on Jan. 1 (ABC, 4:30 p.m. ET) in Pasadena, Calif.
Buckeyes head coach Jim Tressel told reporters Monday afternoon in Columbus that he expected to receive final semester grades for his players later that day. Asked if any players were in major jeopardy, Tressel said, "I assume everyone's in major jeopardy until I see [the grades]."
Carter is the son of former Ohio State and NFL star receiver Cris Carter, who is an ESPN NFL studio analyst.
Adam Rittenberg covers Big Ten football for ESPN.com. He can be reached at firstname.lastname@example.org.