The 24-year-old Danish stopper is under contract with the Royals until June 2015.
Andersen spent the first four months of this season on loan at Portsmouth, but he wants to leave the club on a permanent basis rather than go out on loan again.
"So you could say that I'm forced to put my own ambitions on hold to cater for Reading's needs.
"I've had offers from Denmark, which would have been nice as it would have given me a platform to show that I have what it takes. And I had an offer from Trabzonspor, which would have been interesting as they are a huge club playing in Europe.
"It would have been easier to take if I had played and done badly, but that is not the case. I've always been happy at Reading as they have ensured that my development has been good but I want to play now.
"They haven't promised me anything but I hope I can leave in the summer so I can sleep in the same bed every night instead of being loaned out all the time."
Andersen, who has represented Denmark at Under-21 level, has yet to make his debut for Reading.