The 22-year-old has been training with the Tigers in recent weeks following his release from Arsenal at the end of last season.
The Irish midfielder scored for Hull's Under-21 side in their victory over Doncaster Rovers recently, and Clemence is eager to have Henderson at the KC Stadium.
"Conor Henderson is someone we've had in training for the last couple of weeks," Clemence told the Hull Daily Mail. "He didn't quite make the grade at Arsenal, but he's always had a lot of potential.
"He's had a couple of knee injuries that have slowed down his progress.
"There's more to come from him. He scored a free kick and played some lovely passes around the pitch so we've been impressed. He's someone we'll look to try and do something with to get him in on a permanent basis."
Henderson came through the ranks at Arsenal before signing his first professional terms for the Premier League club in 2010.