The Hoops youngster, 20, has featured just twice this season for his club this season and admits he is growing frustrated.
The former Rangers trainee is not ready to throw in the towel yet with the Scottish champions and has vowed to convince boss Lennon he is worth a place in his Parkhead squad.
The Scotland Under-21 international said: "I'm not too concerned about things at the minute. We have a good squad at Celtic and are in the Champions League, so it's a big time for the club. The manager will want to play his strongest XI and if I'm not involved, then so be it. I just need to keep working hard.
"But you need to play [eventually]. It's no good sitting on the bench every week or in the stands. The older you get, you want to play even more.
"I'm at a big club like Celtic, so I can't really complain, but I do want to play. Is a loan deal in January something I'd consider? Who knows? I don't know what will happen. I'll just have to keep trying to impress the manager in training and see where that takes me."
McGeouch was linked with loan moves to Motherwell, Ross County and Hibernian in the summer and played the final four minutes of the Champions League qualifier against Cliftonville in Belfast in July before starting in the Glasgow giants' shock League Cup defeat to Morton last month.
His only other action this season has been for Billy Stark's Scotland Under-21 side and McGeouch admits he is struggling to come to terms with his lack of opportunities.
"I've not played as much as I would have liked to," he said. "But I did get some game time for Scotland against Slovakia on Thursday and that was excellent for me.
"I've just tried to get on with it and play as well as I can in every game I'm involved in. Hopefully that will help me take my chance when it comes."