Newell's Old Boys have confirmed the signing of Sunderland striker Ignacio Scocco.
Edinson Cavani says he is settled at PSG but admits anything could happen amid reported interest from Manchester United.
The news is a huge blow to manager Craig Brown's attempts to transform the team's fortunes.
Fraser has been a revelation this season, despite being hit by a number of niggling injuries, but his contract expires at the end of the campaign.
Brown told Aberdeen's official website: "The club made the player what was the best offer they possibly could and it's very disappointing that he has chosen to see his future elsewhere.
"It was indicated to the club that Ryan believes he is ready to play at a higher level than the SPL and I have to say I think that is the wrong decision.
"He would be far better to continue to learn his trade here with Aberdeen and I only want players here who are 100% committed to Aberdeen Football Club."
Fraser has made only 21 appearances for the Dons, most of them this season, since making his debut aged 16.
He now looks set to be the latest in a series of promising talents who have left the club in their teenage years, and the club may look to cash in next month.
Scotland Under-19 defender Jack Grimmer left Pittodrie for Fulham in January having played just four first-team games and 19-year-old Fraser Fyvie signed for Wigan in the summer after rejecting an offer from the Dons.