The 19-year-old joined Inter from Feyenoord 12 months ago in a deal worth three million euros.
The Holland Under-21 player, who scored just one goal in six league appearances for Inter this season, is a reported target of Liverpool.
"Inter wants to loan me to an Italian club or sell me," Castaignos said to Sky Italia. "I told them that I don't want to play anywhere else in Italy but at Inter.
"I came to Italy to wear the Nerazzurri colours and not play for any other club.
"Now I must go and Inter will help me find a club.
"I am saddened, I cannot deny it, I am disappointed not to have shown my worth, but this is football.
"It's a decision taken by the club and by me.
"Now I want to join a big club."
Castaignos is under contract with Inter until June 2016.