Maybe other parents are having this problem, and it sounds strange to ask. We have a 4-year-old who cannot tie his shoes. He goes to his older sister or to one of us to have them tied.
We wonder if he has some kind of problem with seeing and doing things. He seems perfectly fine otherwise and is a great kid.
Smart kid. He has others doing things for him, but refusing to help him is not an option.
The answer is to teach him how to tie his shoes, or anything else which requires the fine motor skill. By the way, this is not a uncommon problem at his age and eventually would be a skill he would likely master.
Here is something I learned from another child. Let me share it with you.
Take the cord from a bath robe. They usually are fluffy and easily handled. Wrap the cord around a door knob. Make this a fun experience. Introduce it as something new he might learn. Please do not make him think he is failing with "big boy" comments.
Then in easy steps have him do what you do with the cord by making a bow knot.
Usually a child will master this with a few tries. The texture and ease of manipulation help. Over time show him the same pattern on his shoes.
If all else fails, wait for kindergarten and first grade when socialization helps. If he resists, there are shoes with no laces .