Strachan said: "Alexander will know that 18 months ago we enquired about him.
"Dortmund didn't want to sell him and the price was a bit steep. But he's still on our radar."
Frei, 28, said he was aware of Celtic's interest and they should contact him.
Strachan added: "He's still on our radar, still a good player, but we have a few. It's a maybe."