The striker is currently on a three-month loan from Crystal Palace which expires in November.
However, Town have now contacted Palace in a bid to secure Kabba's services for the complete first division season.
Player-boss Paul Groves said: "Stephen has done very well and we'd love to keep him for the rest of the season."
Kabba has scored only one goal during his spell at Blundell Park, a brilliant solo effort in the 3-2 defeat at Coventry City.