Can I install stapled down 3/4 inch hardwood flooring over existing parquet flooring? I have tried to get the parquet up but it is very difficult because it is glued. The existing parquet is glued to a wooden subfloor which is above grade.

Glued down to what? Concrete? Plywood? OSB?

As long as the parquet is very firmly attached, you should be able to install over it. How thick is the parquet? Is it solid wood or engineered, like plywood?

Gary, not sure if it's it's solid or engineered. It is in finger pieces 1 inch by 5 inch pieces. 5 pieces make a square. The thinckness is a little thicker than 1/4 inch

You have a "finger block parquet". It is 5/16" thick and solid oak fingers/slats. While not ideal, you can install a 3/4" solid over those. Use the same basic install procedures as if going over any wood subfloor. Use 2" fasteners. Double check that all the parquet is well glued down. Re-glue any loose pieces.. Make sure the existing parquet isn't installed over a particle board underlayment. If it is, you will need to remove everything, down to the subfloor. If the parquet is installed over ANY underlayment, my preference would be to remove everything down to the subfloor.

Ya, I would remove it. One of the problems with that parquet is it is mostly edge grain, and when you nail through it, a lot of slats will split. If either side of the split comes loose from the subfloor, you have a squeak you can't get rid of.
Nailed over a parquet floor, once.

Ah-ha, I see you edited the original post, instead of replying to my reply!
Here I was waiting for an answer... Hehehehe.

Austin i am new on here if i new how to reply to you directly i would have lol thanks for the info

Do not do it. I just looked at a job that was nailed down over parquet, and when the wood expanded it ripped the parquet up. Now the customer has a giant speed bump in the middle of the livingroom. It may be more work now to remove the parquet but it will be easier and cheaper then if you have to rip it up along with the new hardwood.