The young Swede impressed in their friendly win over Preston North End.
Rodgers told liverpoolfc.com: "They've seen Raheem progress from a youngster, and that gives them all hope.
"They know that if they do well and show the personality and commitment to play for Liverpool [they'll get a chance] - and they're here because they have quality.
"For example, young Kristoffer Peterson has come in and got two goals. I said to him, 'You'll now come to America on the back of what you've done in your training'. That's what I always judge players on. I look at them to see if they work well, work hard and work with quality, and if they have the personality to play for Liverpool.
"He's been rewarded for that, he'll come to America and hopefully he can continue scoring goals, which is great for him."
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