Help diagnosing source of basement moisture
Can downspout be the issue?


For sure. You definitely don't want the downspout dumping at the foundation line. Ideally you'd have it exit several feet away from your foundation (via an elbow or a splash block or what have you). 

Ultimately, the water has to be carried away from that corner of your property. Does your property slope away from that corner or is that a possible place where water is collecting from other parts of the property? 

You may need to put in some surface drains to migrate that water to a lower part of the property. I'd also check to see if you can find out how high the water table is on your property. Alas, you can't do much about high water tables.