Webb, 30, spent the preseason with the Carolina Panthers before being part of 53-man roster cuts. He has not thrown an NFL pass since the 2011 season and has been used more as a receiver and return man in recent years with the Minnesota Vikings until 2013 and in Carolina through last season.
Bills coach Sean McDermott told reporters Taylor is improving but remains in the concussion protocol after being injured in the team's third preseason game. He expressed confidence in rookie Nathan Peterman being able to start in Taylor's place but did not commit to a time frame for naming a starter.
"We'll cross that road when we come to it at this point," McDermott said. "We feel good we'll have clarity around the situation when we need it, and this team's ready."
Taylor returned to practice on Monday as he continues to go through the concussion protocol, per the team.
Primary backup T.J. Yates is also in the concussion protocol after being hurt in the third preseason game. Peterman was a fifth-round pick out of Pittsburgh.
Taylor has been the Bills' primary starter each of the last two seasons.