The 36-year-old veteran of three World Cups, who has a drinking habit, missed Wednesday's first practice of the summer recess, turning up on Thursday but slinking away without speaking to reporters.
"It's true Ortega won't be staying at River," a club source who asked to remain anonymous told Reuters.
"They told me they would not be taking me into account," Ortega was later quoted as saying on the sports daily Ole's website when asked whether he would be part of the team for the championship starting next month.
"I've got to speak to (club president Daniel) Passarella to discuss rescinding my (contract)," added Ortega.
Local media said coach JJ Lopez had told Ortega he was not in his plans for the Clausura, the second of two championships in the 2010/11 season, due to the forward's "lack of commitment to the team".
A temperamental, skilled ball player nicknamed 'Burrito' (little donkey) with mesmerising dribbling and feints and brilliant goals from chips and set pieces, Ortega played for Valencia, Sampdoria and Parma during a not too successful spell in Europe from 1997 to 2000.
