The Swede has just returned from a loan spell with Tranmere Rovers.
"It feels terrific," Peterson told Fotbollskanalen.se. "It is actually kind of a shock. A few months ago I didn't believe this would happen.
"Brendan [Rodgers] wanted me to sign a contract as soon as possible. It was me and two others who got new contracts.
"This is the biggest motivation boost in my career. This is the biggest I have ever experienced."
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