Memphis athletic director R.C. Johnson defended the men’s basketball program Thursday, saying the school checks out all potential players.

He would not confirm that Derrick Rose, who led Memphis to the 2008 national title game, is at the center of an NCAA investigation of major violations during that season.

In a letter to the school the NCAA says an unknown person took the SAT for a player, with his knowledge, and then the player used that test to get into Memphis. The NCAA said the athlete in question played for the Tigers in the 2007-08 season and the 2008 NCAA tournament. The only person who played just that season was Rose.

‘‘We wouldn’t play anybody if we hadn’t checked it out pretty thoroughly,’’ Johnson told The Associated Press.

Johnson would not identify the player involved for privacy reasons. But he said the player is cooperating with Memphis’ investigation into the allegations.

‘‘Nobody has thrown up any road blocks,’’ Johnson said. ‘‘We’re trying to get it resolved and do it the right way.’’

The NCAA has asked Memphis to provide copies of the SAT and a Sept. 2, 2008, report by a forensic document examiner who studied the handwriting in the SAT.

Rose’s attorney, Daneil E. Reidy, said in a statement Thursday that the No. 1 pick in the 2008 NBA draft by Chicago and this season’s rookie of the year was aware of the allegations.

‘‘Mr. Rose cooperated fully with the University of Memphis’ athletic and legal departments’ investigation of this issue when he was a student and that investigation uncovered no wrong-doing on his part,’’ Reidy said. ‘‘At this time, Mr. Rose sees no reason to engage in further discussion regarding this matter and will instead focus on his career as a professional basketball player.

‘‘Neither Mr. Rose nor I will have further comment.’’

The Chicago Sun-Times reported Thursday that someone with access to Rose’s academic records at Simeon High School changed a D to a C on his transcript. The newspaper reported that Rose was one of our athletes at the school whose grades were boosted for a one-month period after their June 2007 graduation and then changed back after the bogus transcripts were sent to colleges.