My research suggests that it's a monitor fault. To confirm, try to borrow another monitor or even a TV with a PC VGA port.
If a different monitor doesn't have that problem then your ASUS one is faulty. If it's still under warranty I would pursue a claim for repair or replacement, but not until you've confirmed that a different monitor is free from the problem on the same computer.
Also might be worth checking that there are no strong magnetic fields (eg large speaker) on right-side of monitor, though usually that would cause distortion not a colour tint.