If you are new to GSDs, normal behavior is that they want to be touched all the time and will find some way to touch you even when you are sitting down ignoring them. A GSD head on your foot while you surf the web is entirely normal. I don't think I have ever seen one that really didn't want to be touched by its own family. Also standard behavior is wanting to walk between your legs repeatedly -- a full body hug from their point of view.
It could be the same thing my male showed. I got last pick of the litter and he (the largest) was the last because he was shy when approached by strangers. People picking out puppies usually go for the eager ones first. He was shy and hesitant with me for a while when I got him home. Now, of course, it is quite different. I have to move his 100+ pound body out of my lap in order to write this.
It took a few weeks for my male to get over it. I don't remember how long but it could have been a month or a little more. There are times when the dog must be touched, so you have to get them used to that as quickly as possible. My approach is to just act like I normally would with a dog. There are times that I have to wash him or groom him, so I did that as I normally would, and still do today. If he protests, I simply talk to him and tell him that it isn't that bad, like you would do with a kid. It didn't take long before he understood that me touching him was never going to be unpleasant.
I would probably also do something like sit quietly on the couch watching TV and occasionally randomly offer him a treat, if he wants to come get it. First, he has to come to my side. Then, he has to touch me, put his paw on my leg or something. And finally, he has to crawl into my lap (even at 100+ pounds) to get it. He will get the idea. Mine is still quite shy with strangers, but a typical GSD to the family.
As always, be careful what you want, because you may actually get it. Now let me push this beast out of my lap so I can post this message.