That's an old question I've replied to many times in the past. Unfortunately it's not possible. Please allow me to copy and paste the reply I was giving in May and June when asked this question (the original reply is 5 paragraphs long, the following is pretty much the executive summary):
If you are receiving update emails and wish them to stop, please unpublish the System - Akeeba Backup Update Check plugin.
Why do older versions report there's an update available even if it's not supported? This has to do with the Live Update system in use by our software. Older versions of Live Update were not aware of Joomla! version compatibility of available versions of our components, therefore they would report any available newer version as an update you have to install. Changing that required a major change in Live Update and our update server. The change made it in Akeeba Backup 3.5.0 and our other components released after that date. Unfortunately older versions' Live Update code cannot be updated for obvious objective reasons. Releasing updates for older Joomla! versions is also not an option, as it would cause several issues on Joomla! 2.5 sites. Therefore you just have to make sure that you have the latest available release designed for your Joomla! version, as per our Version Compatibility page at https://www.akeebabackup.com/compatibility.html and ignore Live Update's prompts for updating Akeeba Backup.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!