A good way to do this is to get on their radar in different ways. They're bound to be on social media, and almost all of them are on Twitter. So you should follow them there. If they do follow you back that's a good sign, but it's only the beginning. All it means is that they have seen your profile and have quickly decided you're worth following back. They still don't really know who you are.
If they don't follow back, no matter. You can still get on their radar eventually.
What you should do in both cases is retweet their tweets from time to time. And you should also mention them. Again, it's a good sign if they reply or thank you.
Now at the same time you should start appearing in their comment threads. Make sure that you offer really good, relevant insights, of course. Then make sure to tweet each post you contribute to, including their handle in it so they get notified on Twitter as well.
It's this double whammy effect that will make you stand out amongst their many followers and commenters.
Of course you can go a bit overboard with this. It would border on creepy if you did it absolutely every time they wrote a blog post! But if you did it once or twice a week for a month, then had a break, then did it again for a while it wouldn't seem desperate. And they'd have a very good idea of who you are, what you do and they will almost certainly have looked at your blog.
Unless they're super-picky and only follow other A-listers on Twitter then you'll probably have them following you back if they didn't before, too. Also, they may even mention you in a tweet and or/post as one of their top engagers/commenters. And if they do offer guest posts on their blog then you'll be much more likely to have your submission accepted (as long as it's good, of course!).