Wilson became the youngest player to represent Wales when he came on as a substitute against Belgium. While admitting that the 16-year-old could have a promising future at Anfield, Rodgers has made it clear that he will allow the midfielder to develop in his own time.
The 40-year-old told reporters: "He's a very talented young player. To have him here at the club is brilliant.
"I was first aware [that Wilson could play for Wales] when I had a call from Ian Rush to say that he had done well in training and that Chris Coleman was very pleased with how he had been, and the possibilities of having him involved. It escalated from there. He did well in training and was then put into the squad.
"He's a very talented young player that knows he'll have a great opportunity here if he continues to develop at Liverpool. It's important that we just stay calm and let him develop at his own rate."
Wilson has featured for the Liverpool Under-18 side this season.