He is naming one school, however.
"I do (have a list), but I'm comfortable with saying that Ohio State is my leader," he told BuckeyeSports.com.
The 6-1, 180-pound prospect from Palmdale, Ca., arrived back home August 7 after a whirlwind visit to check out the Buckeyes while accompanied by his parents.
"It was far away, so I wanted my parents to get a chance to make sure that they get out there and see it," he said. "I got to do everything. As soon as I got there, they had an itinerary planned for us, from the academic meetings to watching their last little conditioning circuit before they hit camp. We visited the dorms too. Everything was great about the trip."
The plan is to take one more unofficial visit this fall before taking a few official visits. The final unofficial trip will be to the University of Washington to see the Huskies host LSU on Sept. 5th.
As for his planned official visits, Shaw remained somewhat mum on the topic.
"I have Ohio State set up for the USC game, I have LSU and Notre Dame and I'm still searching for the last two," he said, adding that Michigan could join that list as well. He plans to announce his final decision on Christmas day.
Shaw plans on graduating early and enrolling in college courses during the winter. While in Columbus, he met with OSU head coach Jim Tressel and learned he could enroll for winter courses in January or wait for spring classes to begin in March.
He also spent time with OSU cornerbacks coach Taver Johnson, who has a niece who recently graduated from Palmdale. The two went to dinner along with Shaw's parents.
"That was very beneficial," Shaw said of meeting with Johnson.
Shaw said he was impressed with how hard the Buckeyes worked in their conditioning session, which was a final tune-up before the start of fall camp. Afterward, he got to spend some time with a few players including sophomore safety Nate Oliver.
"He was real cool," Shaw said. "Players aren't going to lie to you. They're going to tell you how it really is and he had no negative feedback toward the university or the community or anything like that. It was nice.
"I like that I got to meet a lot of the players because that's who I would be playing with. Having a good feel for those guys was great."
Reflecting on the visit as a whole, Shaw did have one negative thing to say about Columbus.
"I have nothing bad to say except that they say it gets real cold in December and January but I'm not too worried about that," he said with a laugh. "Everything was good."