The highly-rated 22-year-old has only made one appearance since having knee surgery last October and manager Steve Bruce believes a temporary spell elsewhere would be in his best interests.
Barnsley have previously expressed an interest in taking him on loan but a hamstring problem has put a possible deal on hold.
Dudgeon's current contract with the Tigers expires at the end of the season and Bruce is keen to assess his potential.
"Joe Dudgeon needs to go and play somewhere but unfortunately he's hurt his hamstring," Bruce said in the Hull Daily Mail.
"He's training again, probably today, and will carry on next week but he needs to go and play. He needs as many games of football as he can after being out for a year.
"There was a little nibble from Barnsley but unfortunately he picked up a hamstring injury so it wasn't possible."