No, you should stick to a 2XXX series i5 , 3XXX if you have updated the bios to ivy bridge.
NO 4XXX cpu will work on that motherboard.
I would buy a used 2320 or 2400 i5 just because they are cheap.
If you have the latest bios a used i5 3330 is also often cheap.
http://www.cpu-upgrade.com/mb-Gigabyte/GA-P61A-D3%28rev._2.0%29.html
a 3570 would give you~similar performance to a 4590.
Check your bios version against the provided list as well.