The Sox only have Narvaez under contract for next year and an upgrade is needed at the position.

Alex Avila and Dioner Navarro have not been very good this season. Avila is slightly better than Navarro, but he has had two DL stints. He has also come across a setback in the second stint, and doesn’t have a timetable for return. With a lack of internal catching options, the team’s depth issues have been more apparent recently.
If the White Sox do go with Narvaez, they need to play him everyday. They need to know if they have a viable catcher in him, because they have no options left. Instead of resigning either Navarro or Avila, they need to find a catcher in free agency.
Jonathan Lucroy has a club option, so unless the Rangers don’t bring him back, he’s a great option. Lucroy shouldn’t be their number one target though. It should be Wilson Ramos. He’s had a great year. Ramos is a free agent and the White Sox should go all in, because there is no fallback. Lucroy not returning to the Rangers is a longshot, and after these catchers, the next option is nowhere near as good. Ramos is one of the better free agents though, so they need to be willing to spend a lot of money.