The 20-year-old West Ham starlet is one of several players, including Peter Sweeney and Barry Conlon, that the club want to keep at Blundell Park.
"Joe is a great lad around the building, he's a good character," Fenty told Grimsby's official website. "The feeling is that he wants to be here and we have now got to sit down with him. The end of the season is coming and we'll be doing that.
"Ultimately these judgements are for the manager to make. We can all rant and rave about individual players but when all is said and done the manager will decide what he wants here and we'll look to support him as best we can."
Fenty has also disclosed that progress on the club's proposed new stadium at Great Coates is ongoing and that he is "working on some interesting things that could advance the program."