The 22-year-old defender, who joined Celtic from Dundee in January, made his international debut in the 1-0 friendly win over Hungary on Tuesday.
Rodgers said: “Jack came in from Dundee and settled in very well. He has the qualities to play for Celtic and the international team for the next 10 years or so.
“His profile suits the highest level. He is quick, first and foremost, he can defend and in international football it is important that you can deal with the ball and I think you saw his comfort. For a player making his first appearance away from home in the international stage, he was very composed and looked as if he had played a lot more games than what he had done.”