Bazoer has established himself as a regular in the Ajax first team and won his second Netherlands cap on Friday in a 3-2 defeat to France.
The 19-year-old could feature again against England on Tuesday and international team-mate Clasie, who joined Southampton last July, believes Bazoer can become one of Europe's best.
"He's got everything that a good midfielder needs for a top club," Clasie was quoted as saying by the British media.
"He's got power, he's strong, he's fast. Physically he's good. He reads the game.
"He will be an unbelievable player in a few years.
"If you saw some of the games from Ajax, you see that sometimes he runs the whole game for them.
"He scores a lot of good goals, he's got confidence, he shows quality nearly every week.
"In a few more years, I think he will be at the top.
"He is consistent, that is also important to be a good player — that you do not play one or two good games in a year but stay on a good level."