Laurie, Lucia and TF are right. He has a tiny attention span. And he thinks you are the most fascinating and important thing in the world right now, so go with that.
Please talk to your pediatrician about what a child this age is capable of doing; he is still far too young to be expected to play solo for more than a minute or two. As soon as his attention shifts -- in a minute or two! -- he will wonder what interesting thing you're doing instead. This is normal.
Please get some child development books, maybe the "what to expect" book that covers the toddler years, to find out more about age-appropriate expectations for your child. You're expecting him to work on behaviors that he is not developmentally ready for yet. Interacting with you is how he is learning. He WILL learn to play independently, but if you "enforce" it too early, he will only be clingier for longer; let him interact with you all he needs to right now. Kids learn independence and confidence by feeliing secure first; playing with him adds to his sense of security and confidence.
If you want, instead of getting down and playing with toys with him all the time, engage him in what you're already doing: If you're working in the kitchen, give him pots and wooden spoons and let him sit on the floor and "stir," or give him dry pasta in a huge baking sheet to push around with his toy truck. If you're cleaning, make it into a game with him "dusting" something unbreakable. And so on. But he needs this time with you now or he will only take longer to learn independence. Don't push him into it too soon. And please don't "enforce" anything, but do encourage everything.