Midfielder Henderson, 22, is a free agent after being released by Arsenal at the end of last season and so is able to sign outside of the transfer window.
Australian Fletcher, 20, is also without a club after previous spells with Sunderland's academy, Sheffield Wednesday and Cambridge United.
The pair have been training with the Tigers' development squad in recent weeks and caught the eye for their reserves during a 4-0 win over their Doncaster counterparts on Tuesday, with both players getting on the scoresheet.
Reserve team boss Stephen Clemence has been impressed with the young duo and confirmed they may now be offered permanent deals.
"Conor Henderson is someone we've had in training for the last couple of weeks. He didn't quite make the grade at Arsenal, but he's always had a lot of potential," he told the Hull Daily Mail.
"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.
"Matthew Fletcher is another one we'll look to talk to in the next couple of days. I had him at Sunderland as an 18-year-old. He's an Australian boy who's gone to a few other clubs since then.
"I think he's come on and improved, so he could be someone that can help the group."