The Sky Bet League 1 club face Arsenal in the fourth round of the FA Cup tomorrow night and are optimistic that McGeouch will be in the squad ahead of the tie.
The 21-year-old midfielder has made just three appearances for Celtic this season, while his only start came in a Scottish League Cup defeat at home to SPFL Championship team Morton.
Coventry have been linked with a move for the Scotland Under-21 player already this season and it is understood that any move now could later become permanent.
"We're quite close," said Steven Pressley, the Coventry manager. "I'd like to get him in the group because we have a lot of games in February."