"He's got a lot of raw talent," White said from his gym ... "He looked good in his showing there."

White says he wants to get Hardy more experience before he puts the ex-NFL star on the main UFC stage -- and the ideal situation would be a second fight in his Tuesday Night Contender Series.

"In a perfect world what I'd love to do is turn him around and have him fight again in the last fight of the Contender Series."

FYI, the series finale is reportedly set for August 7 ... which would give Hardy exactly 8 weeks to prep.

White says if Hardy wins that fight, he'd still like to see him rack up a few more wins before he gets a major UFC fight.

As to the criticism that comes with signing Hardy -- who was convicted of domestic violence (which was later overturned when Hardy appealed) ... White says he's ready for it.

"What I respect about the guy is he did something really bad and horrible. He went through everything you need to go though after you do something disgusting like that. Then he hit rock bottom, picked himself back up, started to work his way up to become not only a better human being but a better athlete."