The 22-year-old defender has now played four games for the club since he joined prior to the game against FC Halifax Town in October and Mariners` boss Paul Hurst was keen to keep the loanee defender at Blundell Park.
Hurst said: "Conor would clearly like to play as high as possible, he's played higher than where he is currently at so I've got no qualms whatsoever with that and understand his thinking.
''As his manager apparently said, he needs to try and carve out a career and at the minute it's looking extremely difficult to be getting into Hull City's first-team.
''They're doing extremely well and are only just down from the Premiership so it is probably a big ask for Conor but I do think he's got good quality.
''I'm sure he will have a good career, it's just a case of where that ends up being.
"I think it's a better Conor Townsend than we had a few years ago. He's brought composure, he brought quality, he brought a drive," he added.