Hello!
Former intern here (granted it was almost 4 years ago!)... It depends on your market and when the major colleges and universities have job fairs in the Spring Semester. If I remember correctly, I had completed my interviews at this point and was awaiting final decision... But my university always had their job fairs in mid-January, so maybe the process moved faster because of this.
However, if you live in a less popular market, they will accept applications a couple weeks out from the internship start date (usually mid/end of May). I'm connected with two intern recruiters on LinkedIn, and they have posted internship job posts into late April.