One, an offer has been made, and Taylor's agent is shopping around to see if there will be any market for his client - a 35-year-old veteran cornerback who's season didn't end as well as it began.
Two, no offer has been made, because the team isn't planning on bringing him back at all, and they are preparing for his release, along with juggling the other administrative tasks that come during the Paperwork Week of the NFL calendar.
Or, perhaps a third option exists; it's being announced as I write this.
Let's say it's not, and let's just entertain the very remote possibility veteran free agent cornerback Alterraun Verner is moved by his past connections to Steelers defensive backs coach Carnell Lake (coached him at UCLA) and offensive line coach Mike Munchak (his head coach with the Titans). The availability of funds to pay Verner would, logically, come through the removal of a player at his position - Taylor. Asking Taylor to take a pay cut is an option, but the real reason they would ask that would be if they needed him on the Steelers team in 2014. If Verner was an option, perhaps they wouldn't offer, they would just release him, freeing up more money against the cap, and theoretically, affording them the opportunity to make a more competitive offer for Verner.
All a stretch, to be sure. But it's one possible explanation behind why the move hasn't been made on Taylor yet. It's still something that is expected to happen, and likely will at some point soon - with not commitment being made to a date.
Otherwise, all is quiet, but roster moves should be expected over the next day and change before the official start of free agency.