Why is my Joomla! 2.5 site update manager showing an update to 3.x?
From Joomla! Documentation
Revision as of 18:05, 2 August 2016 by FuzzyBot (Importing a new version from external source)
Not unless you’re 1000% sure. By default, Joomla will not let you update to 3.x unless you activate the option within the Joomla! Update component (administrator >> Component >> Joomla! Update >> Options >> Update server >> Short Term Support). If for some reason you’ve changed this, and you’d like the updater to stop letting you upgrade, change the setting to Long Term Support. After making this change, you’ll only receive updates for Joomla! 2.5.
Notice: You should not upgrade from Joomla! 2.5 to Joomla! 3.x unless you are certain that all of your additionally installed extensions (from third party developers), especially templates, are Joomla! 3.x ready or have a Joomla! 3.x version that you can upgrade to. You should only upgrade from 2.5 to 3.x on a development site not on your live site. See Why Migrate and follow the pages for more information on upgrading from 2.5 to 3.x.