The Sun says the 18-year-old England youth cap is a free agent at the end of his breakthrough season at Rams.
Winger Ebiowei burst into Roo's side this season as they battled for survival in the Championship.
And the teenager alerted has plenty of clubs with his skill and speed.
Palace have made a decisive move, however, and want to land Ebiowei from the Rams just as they did with Luke Plange, 19, another ex-Arsenal academy prospect.
Boss Patrick Vieira sees the pair as long-term prospects and may look to loan them out next term.
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