If the Titans aren't going to franchise Alterraun Verner, then the best they can hope for is to get him under contract for around $9.5 million, which would make him a top-10 paid cornerback in the league (based on this).
It is all well and good to say that the Titans should spend that money, but what else could the Titans spend that on if they didn't sign Verner?
With that $9.5 million, the Titans could afford to spend $2.5 million on Ropati Pitoitua, $3 million on Bernard Pollard, and $2.5 million on Damian Williams. That would essentially solidify the Titans defensive line, defensive backfield, and add significant depth to an already talented receiving group.
Also, the alternative at cornerback isn't the end of the world. Ray Horton should be capable of finding a full-time starter between Coty Sensabagh, Tommie Campbell and Blidi Wreh-Wilson. If not, free agency is filled with corners with a less impressive resume but a similar skill set to what the new coaching staff will look for.
When you have a free agent the caliber of Verner, you have to consider the market and the impact he will have on the team. Is he a player that will get the Titans to the playoffs next year? Probably not. Is he irreplaceable? Probably not. Is he a young player that can be a cornerstone of the team? Probably.
So can you justify spending that much money on a position with such a short shelf life and a high price tag? Or would you rather fill some other areas of need and trust your drafting?