Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
Hunt, who has been linked with a move to Brighton, is out of contract and has confirmed that he will not be staying on.
Hunt wrote on Twitter: "On a personal note I would like to thank Nigel (Adkins), Andy (Crosby) and all the staff at Reading FC, especially Sir John Madjeski for the five wonderful years I spent at this wonderful football club!
"The last week was very emotional for me and I would like to take this minute to say thank you very much to the Reading FC fans! You have been nothing but amazing to me since I arrived five years ago and for that I thank you sincerely.
"We have had our ups and downs in this time but we had them together as not just players and fans but as people and friends together!
"I have no doubt that Reading FC will bounce back to the top flight with the great people at the club! And on this note I bid you all fair well."