How can I fix theses white spots...

The chessboard was near a window and the sun seems to have burned some boxes (white circles on the squares).
Can someone suggest some ideas to fix this?

Thanks!

Keep them - it adds a bit of patina and character. My darker squares on my board has been sun bleached because like yours, it has been sitting on a table near a window for several years. I just like the look of it . . . 

Is the board coated/varnished/waxed in any way - if so it may be the coating that is damaged rather than the board itself.

It could also be a reaction to being cleaned with chemicals of some  sort while dusting it.

It looks like the sun has darkened the wood where the pieces weren’t, leaving the lighter circles which is the original colour. I suppose if you get in the habit of clearing away the pieces the white circles will diminish over time.

is it solid or veneer?

varnished or just oil or finish?

I got a Drueke board marked like that...

I toke it around people to see if it can be fixed... basically it comes down to sand it a bit and refinish it... I just leave lit like that.

it might be the finish discolouring from UV exposure, but its more likely to be the pale timber darkening with exposure to UV and oxygen which will penetrate a small distance into the wood and that looks veneered (and modern veneers are quite thin).  I'd go with Ipswitch's advice and try to get the darkening of the pale squares to even out over time. 

WOW - it must have been sitting there as an ornament and obviously never played with at your window for quite a considerable time to have received that much damage. Which leads to another bug bear of mine - Chess Sets as Ornaments ! ! ! They are not ornaments, they are to be played with . . . 

?

I don't think its damage, I think its unevenly aged and just means that its been stored where it will get some sun.  Playing with it, unless done obsessively all day, would not prevent the effect caused by the storage location.      

As another poster mentioned, it looks like the board was darkened by the sun in the areas where there were no pieces standing; one idea for a fix would be to cover everything except the white circles and expose the white circles to the sun until they darken enough to match the rest of the board. You could probably use sheets of paper with holes cut out of them to achieve this, but it will require some precision.

The board probably did not cost but a few tens - if at all - of the posters local currency, so just buy another one . . . . You would replace a defective appliance, so why not a Chess Board. As I have said previously, IMHO such wear and tear adds character and a patina to a board . . . 

PS - not even a courtesy reply from OP ref these posters giving their advice. An acknowledgement would be nice . . . 

https://www.coolchesscanada.ca/collections/mid-range-chess-sets-1/products/modern-chess-set-in-golden-rosewood-with-tiger-ebony-board-2-75-king

I bought this chessboard 2 years ago. I left it in the living room for a while without playing with it! I do not want to replace it.
Thanks anyway for your suggestions.

Don't replace it, just don't keep the pieces on it when not in use. In a couple of years I expect you won't be able to see the white circles anymore.