My Ubuntu 15.10 system only reminds me to install Ubuntu 16.04, but I wish to install 16.10 version.
How could I upgrade to 16.10 directly?
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You probably have set in
Software and Upgrades that you should be notified only about new LTS (Long Term Support) versions. Ubuntu 16.04 is a LTS version, Ubuntu 16.10 isn't. You can see the setting you need to check in this blog entry, for example.
But as others have mentioned in answers and comments to this question, you should upgrade to the LTS version 16.04 first, and then in a second step to 16.10.