Strachan believes that the 26-year-old is good enough to play for a top-flight club in England or Scotland.
"The coaching staff scratch our heads and wonder why he is not playing in the English Premier League," Strachan told Sky Sports News.
"He could go to a Celtic or to a club in the English Premier League no bother. He can play different positions too which makes him even more valuable.
"He can play on the left, as he did against Germany, he can play on the right side, he can even play left-back. And he has a love for the game which is so refreshing. He's worked so hard to get where he is right now that he doesn't want to lose it."
Anya joined Watford from Spanish side Granada in July 2013 following a successful loan spell.