Wilson, 19, made his Scotland debut last night against Faroe Islands.
"If Danny follows in Stevie Nicol's footsteps he will be doing well," Lee told liverpoolfc.tv.
"It's great for any of our players to get international recognition at senior level. He has done well at U21 level so this is great for the boy.
"Danny is working very hard at Melwood. He hasn't had the game time that he would have liked but he is trying to improve and he is working hard every day."