The 30-year-old Irish striker has almost single-handedly moved the Mariners to the brink of safety at the foot of League Two, with five goals in six games since moving on loan from Bradford.
And Newell is hopeful that he can agree a deal to bring Conlon to Blundell Park provided his side do not lose their last two games and Chester pick up four points out of six.
"Without a doubt, we'd like him to stay," Newell told the Grimsby Telegraph. "He's given us not just goals but a real presence on the pitch and in the dressing room.
"He's been a real asset to us. It's one we'd look to sort out."
Conlon is also keen to arrange a move to Lincolnshire, adding: "I've already spoken to the manager about it and I'll speak to him again once we know where we are."