Iheanacho was not in his nation's squad for the recent international games.
And he was criticised by Super Eagles manager Gernot Rohr, who felt the 22-year-old was not professional enough.
"When I saw him at Manchester City, he was always a young player that could come in and affect the game," said Rodgers to reporters on Iheanacho.
"Then he's come here with a big price-tag.
"From what I've seen in training and when I've spoken to him, he has shown a wonderful appetite and enthusiasm to get better.
"We have a culture where we want to improve players and make them better and he's responded very well to that."