The promising goalkeeper linked up with the Bhoys in September on an agreement which is initially due to run until the turn of the year.
Oberschmidt is, however, keen to spend the remainder of the current campaign in Scotland.
The German teenager has already graced continental competition for Celtic's U19 side - figuring in a 2-1 defeat to Barcelona in the UEFA Youth League.
The 18-year-old shot-stopper now feels that his future development would be better served by a prolonged stay at Parkhead - as Celtic can provide the perfect stage for his talents.
Oberschmidt said in the Daily Record: "I could maybe extend it to the summer depending on how it goes.
"I hope to get to show good performances and help the club out."