It could be possible but healthy birds sleep on one leg with there head tucked be hind there back. If your bird is tame I would take him out of his cage and place him on the ground and try to get him to walk if he is limping take him to the vet right away. It doesn't take long for a birds leg to heal in a funny way that could coz him to have problems for the rest of his life. If not then place him back in the cage and let him sleep. If he is not tame try to take him out and place him on the floor he will move and then you can see if it is or not

take it to a bird vet asap so he can set his leg right so it will mend...good luck

African grey parrot , 5 years old. He has been standing in the same position on a perch for the last 30 minutes. He has his right leg curled up to his belly in his feathers and he has had pressure on the left leg for at least 30 minutes. It is nearly time where he would usually go to sleep maybe that's why the leg is curled but usually he would be moving around much more. Any advice or other symptoms of a broken leg that could help? Thanks :)