I have not yet received my academic transcripts from my University and the application deadline for a PhD program that I am interested in is already near, and I won't be receiving my transcripts before it. Can I submit my mark sheets to the University? If yes, then should I mention it somewhere that I am submitting my mark sheets instead? And where should I mention it? They have asked for a CV and a cover letter, so those are the two other documents I'll be sending. Or should I first contact the University and find out if it is okay to do so?
Most universities realize final grades aren't available, and will usually accept an partial transcript showing what's been completed up until that time.
However, not all programs will be willing to accept "unofficial" transcripts such as grade sheets and printouts from the registrar's office. If there's a concern on this point, you should contact the specific departments and programs to which you're applying and ask them for guidance.