The Welshman moved to Anfield this summer in a £15m deal, following Rodgers from Swansea City.
The 22-year-old had plenty of pressure following his transfer, with a large price tag and the imminent arrival of his first child, however, Rodgers believes he has done well and "will only get better".
"I think it's remarkable how quickly he has settled," Rodgers told the official club website.
"All of these emotional things have been going on in the background yet he still has come in and made the performances that he has done.
"He looks like he has been a Liverpool player for the last 10 years. He has been outstanding and he will only get better."
Liverpool have yet to pick up their first win in the Premier League this season.