Can I choose to not use rental loss forwarding but keep it, if I don't need it to offset the taxable income this year?

You don't have the option to not use it. Basically, you will still "claim" it. But not to worry, as if your taxable income is already zero, then it will be carried forward. If you don't "claim" it, then you lose it permanently.

if you have taxable income you have to use the passive rental loss unless it is not allowed because your adjusted gross income is too high. look at form 8582.  if it is used, depending on the specific credit it could be lost, refunded anyway, or carried forward.

Thanks!

How do I ‘claim’ it? what form I can see the related data?

Thanks! How do I ‘claim’ it?

All you have to do is enter the sch E information and the unallowed/allowed losses will be calculated automatically by the program.  

How do I ‘claim’ it?

With TurboTax, you can't "not" claim it if you enter all your data correctly in the SCH E section and other parts of the program. The program will automatically carry foward that amount which is not allowed.

I see. Thanks.