Reference manager that sorts by number of citations This question is related to: How to sort search results from SCOPUS or Web of Knowledge by number of citation in a specific field?
but a little bit different.

Is there a citation manager that keeps number of citations current for articles that are found in common databases? I have looked at popular ones like Mendeley, ReadCube, and others but haven't seen this feature.

I think that if number of citations was a field in a manager database, it would probably be easily sortable.
Zotero has a plug-in that will allow you to add a field called 'extra' that contains the number of citations. Keep in mind that the number of citations are taken from google scholar and not from WoS or scopus. But it's a starting point.