To professionally convey that you don't have the time for something at the moment while maintaining sincerity and respect, you can use the following communication:
"Thank you for reaching out, but I must sincerely admit that I'm currently swamped with other pressing commitments. Regrettably, I won't be able to address this matter right now. However, I genuinely appreciate your understanding and would be more than willing to revisit this at a more suitable time in the future."
By using phrases like "sincerely admit" and "regrettably," you're showing sincerity in your response. Additionally, expressing appreciation for their understanding and leaving the door open for future engagement demonstrates professionalism and respect.