Uncertainty over Sunderland and Newcastle duo ahead of January transfer window
Both players joined The Mariners in the summer but are set to return to their parent clubs in January.
Robson, 23, has gained valuable game time this season and has scored three goals in 10 league appearances since his summer move.
Magpies left-back Gibson, 22, has also played regularly for Grimsby this term and has featured 11 times since leaving St James' Park.
For that reason, Limbrick is keen to keep the pair as his side battle to avoid relegation from League Two.
“I think because they’ve come in and settled in well, and had good games for us, we’d love to extend those loans,” Limbrick told Grimsby Live ahead of Saturday’s trip to Carlisle.
“Obviously, they’re players that we borrow, they’re not our players, so we might not have a choice on that.
“If one of the clubs feels that they want to bring them back and play them in their first team, then that’s within their right to do so.
“We’ve agreed the loans until January, we’ll have a look if and when it comes, but they’re two boys we’d like to extend the loans for.”
Robson made a handful of Championship appearances for Sunderland during the 2017/18 Championship campaign before he was loaned out to SPL side Dundee FC last season.