The Middlesex opener was axed prior to the 2013 Ashes series, having scored two centuries and averaging 31.93 in his nine-match run in the Test side.
England have since gone through several alternatives at the top of the order without giving Compton a second chance, and the 31-year-old feels that he has unfinished business with the international game.
He told The Guardian: "It is like being dumped by a girlfriend and you don't think they have given you the real reasons. There is no closure.
"But I am not going to give up hope. I don't want to accept it.
"I feel like I'm in the prime of my career now and I want to kick on again. I thought I was going well and then suddenly you get dropped and spend nights in bed lying awake reflecting."
South African-born Compton, grandson of England great Denis Compton, returned to Middlesex over the winter after five seasons at Somerset.