Saints left a January offer on the table for the 22-year-old but had it rejected by Birmingham, as they looked to push the price up.
He said: “I don't want to discuss any personality.
“We were linked with him in the winter transfer period also.
“We have eyes on a few young players who fit in our shape and philosophy and we are mainly looking for younger players.
“First, we have to be safe."
Hasenhuttl was then asked whether Adams is one of the names on a long list, with the Austrian replying: "Yes."