Officials say there are concerns that the exams are unfair to minority and low-income students.
The Board of Trustees for the 23 campuses will vote in March on recommendations to end the testing requirements.
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They were presented at a meeting Wednesday.
If trustees vote in favor of permanently eliminating the exams, the CSU will join the University of California in having a "test blind" admission process.
The University of California's Board of Regents voted last year to drop the tests at its nine undergraduate campuses.