The Hoops youngster, 20, has featured just twice 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 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 impressing 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 Celtic's first Champions League qualifier against Cliftonville in Belfast back in July before starting 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.
"I want to play in every game that I can. It's not great sitting watching other guys play. It's frustrating to train all week and not play at the weekend. But growing up as a footballer, you have to deal with that."
McGeoch helped the Dark Blues youngsters to a 2-1 win over the Slovakians in Paisley as the Scots got their qualifying bid for Euro 2015 back on track ahead of Tuesday's trip to Georgia.
The team had followed a humiliating 6-0 friendly defeat to England up with another four-goal thrashing by Group 3 rivals Holland last month but McGeoch claims Thursday's victory has restored the team's confidence.
He said: "The England game was really disappointing but the people who were at the Holland game gave us a lot of praise for the way we played. We had a lot of chances at 0-0 and even at 1-0, we had a lot of one-v-ones with the goalie.
"They picked us off in the later stages but gradually we have got better and the Slovakia result shows we are back together, getting results and playing good football.
"Now hopefully we can get a result in Georgia, which will put us on nine points. Holland have won all three of their games so far, so it will be great for us to get as many points as we can and hopefully get up near the top."