Currently, I am a PhD student on paper. However, I would love to apply for a PhD program abroad. I do not intend to finish my current PhD. I am doing nothing for it. I am just a student. However, I have been striving to find a PhD program abroad and become acceptable (money issues, language skills etc.) for a long time. My goals are concrete about my academic development and I feel I am highly motivated. I would love to complete my studies in a more respected university and experience a new academic environment. My current supervisor and former supervisor from MA fully support my decision and intention. In case of getting a certification of acceptance from a new program abroad, I will definitely leave the current program. I have to do that. So, how should I mention or imply on my CV that I will leave my current PhD in case acceptance for a new one?
Your CV is not the right place to mention this. Instead, you should write a brief explanation near the beginning of your personal statement or cover letter which explains your reasons for applying to a new PhD. I would advise that you think carefully about how you explain your motivations. If you sound like an uncommitted student (even if that is down to your environment rather than yourself), a new supervisor or department are unlikely to want to take you on.
Make sure that your CV is an honest record of your past employment and education. You should not omit your current position as a PhD student, even if you aren't really working for it.