Hodgson knows the 23-year-old well from their time together at Liverpool and with England's national team.
He said: “The thing is that when players burst on to the scene very young like Raheem did, everyone starts to rave about them and talk about their potential, and it can very often work against them.
“They need time to get the matches under their belt, time to get the maturity. And last season I began to see signs of his maturity.
“What I am seeing now is a player who still has the same level of ability, the same pace. But what I am also seeing is a much more mature individual who is seeing what being a top Premier League player in a top Premier League team is about.
“What he has done is added goals to his game – by getting into the penalty box a lot more often and that must be credit to the work the club are doing with him."
Hodgson has played a huge part in Sterling's development. He added: “Raheem trained with the first team when I got to Liverpool.
“I gave him his Liverpool debut in a friendly against Borussia Monchengladbach, when he was 15, and I gave him his debut with England as well. Have I been surprised by the impact he has made this season? No, not at all."