The 21-year-old joined The Mariners in late August on a three-month loan deal from fellow Division One side Crystal Palace.
With Kabba's loan spell set to end in late November, the Blundell Park side have contacted Palace in a bid to secure the youngster's services for the rest of the season.
Despite Grimsby sitting at the bottom of the table, Kabba has still been a major hit at the club and his displays have attracted the interest of other Division One clubs.
Nottingham Forest are reported to be monitoring his progress but Palace may be reluctant to let the striker move on.
The Eagles may decide to have Kabba return to Selhurst Park after he appeared in the South London club's first three matches of the new season.
