Ok, as nice as it sounds to just love it....
Ick. You need time and space to yourself.
My daughter did this as well - and it drove me insane. It got to the point where I didn't even want to be around her, because I knew I couldn't have my own space, but instead had to have this hot, wriggly body on me at all times. The more annoyed I got, the more she sensed it, and the more clingy she got. This is not good for anybody.
Incidentally, she's about to turn 8 and she's still more clingy than most children - she always wants to lean on me, sit on me, hold onto me, etc. She even does this at the dinner table, where all of a sudden you'll realize that she's basically leaning over our plates while eating off her own. But, at this point, I just tell her that I need my own space and make her move.
There are 3 things that we did when she was little that worked really well to help us get our own spaces and still give her the connection she needed. She started carrying around a t-shirt that I had slept in for a couple nights. It was soft and she could cuddle it and hold it, and it smelled like me, so she felt that she was close. When the smell started to fade, we would just switch t-shirts.
The other thing we did was get her her own chair that was only hers in the living room. It was her size, and we made a huge deal out of it. Because of that, she was excited to sit in her own space - and it got her out of mine. Thirdly, and I know there are a thousand people who will say that this is the worst thing you can do, I let her sleep in my bed with me. She got all kinds of cuddling time then, and seemed to need a little bit less during the day.
Another thing that you can consider is using tactile type therapy options. These are things that therapists use for children and adults with tactile issues which can help them immensely, but there's really no reason why people without tactile issues can still use them.
One of these things that both my daughter and I love are weighted blankets. The feeling of them really helps to settle and calm and reduces anxiety. They're really expensive, but you can also make them - though it's a little complicated. If you google "weighted blankets" you should be able to find directions or a seller.