Suzuki Reno making weird noise?

I own a 2007 Suzuki Reno with 31,000 miles on it. When I start the car there's a faint grinding noise that I hear from the driver's side of the car. When I accelerate from standstill I can hear the noise. But it slowly disappears when I pick up to speed. It's not a loud noise, but I can hear it. Does anyone know what this noise could possibly be?