Though there is no update in progress, you might unable to update your WordPress site to the newest version of WordPress because you got a message like "Another update is currently in progress". Reload the page, re-try the update process but still experiencing this same message. If this is the situation then this message is incorrect.
It is an automatic lock state to prevent WordPress from simultaneous core updates. Usually, this message will disappear after 15 minutes but if the update is not completed successfully the message won't disappear. So if you want to get rid of that message and upgrade your WordPress site without waiting that long, then follow the steps below.
Let's get rid of another update is currently in progress
Delete the record from options table –
Since WordPress 4.5:
option_name = 'core_updater.lock'
Before WordPress 4.5:
option_name = 'core_updater'