Direct:
John said, "Do you know if Tom plays cricket."
Indirect:
John asked me if I know if Tom plays cricket.
Is it correct grammartically and in terms of spoken English?
Thanks in advance.
I would have written it as "John asked me if I _ knew _ if Tom plays cricket." but it is a fairly tiny difference, and not one that many people would pick up on.
Since 'asked' is past tense, know/knew should be past tense too. Apart from that, it is perfectly normal usage.
Direct: John said, "Do you know if Tom plays cricket?"
Indirect: John asked me if I knew if Tom played cricket.
[ Direct: John says, "Do you know if Tom plays cricket?"
Indirect: John asks me if I know if Tom plays cricket.]