The Swedish winger joined Liverpool at the age of 16 and has impressed during a recent loan spell with League One side Tranmere.
Peterson made six league appearances for the Rovers during a month-long loan deal and also featured in the second round of the FA Cup as Peterborough beat Tranmere 5-0 at London Road.
Although Peterson is yet to make his first-team debut for the Reds, he remains a central figure in the club's Under-21 campaign and is committed to securing a new contract with the club.
"I am fully focused on Liverpool," Peterson told Fotbolldirekt.se.
"There is nothing else. I have a very positive feeling right now and I feel that I deserve that.
"I have worked extremely hard recently and if I continue to work as hard as I can, I know I will get chances."
Before going on loan to Tranmere, Peterson scored once in his three Under-21 Premier League appearance and despite feeling a regular, the 18-year-old admits he would not turn down another loan move.
"I feel that I have earned my place for the reserves and when I play I will show the club what I can do," Peterson added.
"But of course, I don't close any doors and I might consider going on loan again."
Peterson acknowledged the value of his time at Prenton Park and admits the physicality of League One football has developed a new aspect to his game.
"It was a good experience," he claimed. "I need to play first-team football and it was cool to play matches that really matter, with a lot of spectators and so on.
"Everyone who watched me play knows that I am good with the ball and can play the nice game.
"But now I have also started to learn the physical part. In League One it is not the technique that matters so much, but the physical game."