Casey plans to withdraw from the school and likely will miss the 2012-13 season, SI.com reported Tuesday. If charged, he could face a one-year suspension.
By withdrawing from registration, Casey keeps his final year of eligibility and could return to Harvard and rejoin the team once the case is settled.
Curry's father told SI.com that the point guard is weighing his options. However, the Boston Herald reported that Curry also is expected to withdraw from classes.
Harvard announced Aug. 30 it was investigating allegations that 125 undergraduates "may have committed acts of academic dishonesty, ranging from inappropriate collaboration to outright plagiarism, on a take-home final exam" for an introductory government course on Congress.
Casey, Curry and another men's basketball player are among a group of students -- both athletes and non-athletes -- facing charges of academic dishonesty whose cases still are under review, according to SI.com.
Harvard coach Tommy Amaker and spokesman Tim Williamson have not publicly commented on the reports.
The Harvard Crimson, the school's student newspaper, reported that other athletes, including football players, also are among those implicated.
On Wedneday, football coach Tim Murphy declined to comment on specifics. No one has been removed from the football or basketball rosters posted on the athletic department website, and the football coaching staff signed off on a depth chart for Saturday's game, Harvard sports information director Kurt Svoboda said.
"All of our 24 projected starters are in good academic standing," Murphy, who missed Wednesday's football media luncheon for what Svoboda said was a previously scheduled, all-coach admissions meeting, said in a brief telephone interview with The Associated Press. "They are healthy and will be ready to play on Saturday."
Casey and Curry helped lead Harvard to the program's first Ivy League title and to its first NCAA tournament appearance since 1946. The Crimson went 26-5 last season and are the favorites to win the Ivy League in 2012-13.
The 6-foot-7 Casey led the Crimson in scoring last season, averaging 11.4 points per game, and was a first-team All-Ivy League selection.
Curry served as Harvard's primary ballhandler last season, averaging 4.9 assists and 1.6 steals -- both team highs.
Information from The Associated Press was used in this report.