I have lost almost $10K in stock options in the last couple of weeks, can I

[bonthasrinivas]

Can I claim these losses while filling returns for next year?

[SusanY1]

Yes, as long as the options are not held in a retirement account or other tax-deferred account.

If you realize the loss by the sale or expiration of the options they will be deductible losses on your 2020. Capital gain losses are deducted against your realized gains on other capital assets.  If you do not have any gains, you can deduct up to $3,000 of losses against ordinary income in one tax year, with the excess losses carried forward for use in future years. 

[Carl]

in the last couple of weeks,

What happens in 2020 does not count for your 2019 tax return. It's perfectly possible that later in the year you could have gains that will offset those losses.