WLFI-TV and the Journal & Courier report Purdue police arrested Cooper for theft and Rose for attempted theft about 1 a.m. Wednesday on campus. The two players, both 18, were booked into Tippecanoe County Jail and released on bond.
Police Chief John Cox said Thursday he could not release any more details because it was an ongoing investigation.
It wasn't clear if either player has an attorney who might comment.
Purdue athletics spokesman Matt Rector said coach Darrell Hazell was aware of the arrests.
The Boilermakers host Virginia Tech on Saturday.