Can I allow my puppy near my breast?

Keep up the feeds, give the puppy plenty of affection, cuddles and keep it warm.

There's no need for the puppy to play with your breasts per se. Unless you are lactating, in which case a very young animal may be drawn to human breasts, the puppy will not relate human breasts to being fed. The puppy will be looking for comfort and safety.

I'd recommend getting the puppy vet checked and ensure that all its nutritional needs are being met. At some point you will need to address this, as puppies start weaning at around 6 weeks and there is a progression onto solids.

15 days is extremely young for a puppy to be away from its mother, that said it sounds like you ended up with the puppy from a local shelter, so the mother or a surrogate mother may not be available.

If that is a case I would recommend you go that shelter or a veterinarian to find out the best care regimen for the puppy in terms of diet and socialization. This is going to be a difficult time for both you and the puppy as they will require a lot of extra attention.

Related to your direct question, I doubt that the puppy is trying to suckle from you, and I suspect that it is really seeking warmth and comfort, and is just trying to stay as close to you as possible. Young puppies spend most of their time either in a pile with their litter-mates or right up against their mother, so it is just trying to replicate that with you. In order to keep the puppy comfortable and calm you may want to buy a number of warm and soft plush toys that they can snuggle up with to simulate their typical puppy behavior.

Disclaimer: I am not a vet or an expert on puppy well-being, and you should follow any expert advice you can get on the matter

15 days is way too young to separate a puppy from the mother. Like Trond Hansen wrote, the puppy has to eat mother's milk in this age to be healthy and it needs the body of the mum to stay warm and comfortable.

This could be the reason the puppy searches for the body contact with you. The near breast is not its aim I believe, because there is no smell of milk (I assume you have worries about this? Am I right?) in case you are no new mum now.

You write "the puppy is too much attached" but this I assume is normal in this age. Being 15 days old, a puppy has no (really NO) chance to live without the support of other (normally the mum) animals. It knows this and is active searching for protection. It wants to stay close and be sure it is protected by someone against enemies, cold and hunger. Its understanding does not reach through a door, over a "normal" distance or differ between nature and your home. Because of that, it needs short distance to its protectors (you and your family) to feel good and be the best puppy it could be.