1881 US $10 gold, what do you think?

I have been offered this gold piece, I am very unfamiliar with gold and I don't know how to tell a fake, Like with Silver I do the Ice test with gold I don't have any Idea.

 Also what should I pay?

https://en.numista.com/catalogue/pieces16134.html

To my eye it looks like an authentically worn gold coin, but of course it's stuck inside some jewelery. (The jewelery looks old, which is a good sign - if the mount is an authentic antique, then the coin is also likely to be authentic.) Before offering any price, find out if it can be removed. If the coin can be taken out of the jewelery mount without any damage, it will have some numismatic value (not sure how much because I'm not a real American collector). If its edge or rims are obviously damaged from the jewelery mount (or, even worse, it's permanently soldered to the mount) it should only be worth its gold weight.

EDIT: My 2013 Red Book gives these prices for a 1881 (no mintmark) $10 coin:
VF-20 $900
XF-40 $925
AU-50 $950

As you can see, the grade does not really matter: these prices seem to be mostly just dependent on the price of gold. Gold is not as high as it was in 2013. The gold value of a gold $10 coin today is $524.28.

So you may want to ask... $550? $600? Somewhere in there.

I agree with nalaberong on the price.

However, if I was buying it, I'd want to find out if the coin has been damaged by the mount.

I also agree with nalaberong on the price but I wouldn't pay more than $550 even if the coin isn't damaged by the mount. Otherwise $530 seems more than fair because these coins are a dime a dozen, especially in damaged condition.

Thanks for your advice!

 I have offered him, but I don't expect to hear back, he said the melt value was $600 so he was expecting more than that. to me Honest I am scared of gold coins, I don't know anything about them and for $500 I would get piles of bulk world coins.

That coin should very easily remove from that mount, all you need to do is pop the pin up, do it very gently and slowly as not to snap them off. I suggest a set of long nosed pliers with a small amount of electrical tape on the end so as not to leave any marks in the coin is you touch it.