Short would make an estimated $14.77m (£11.9m) if he signs the one-year tender.
A four-year NFL veteran, Short has 17 sacks in the past two seasons (2015-16), third-most among NFL defensive tackles. He had 11 sacks in 2015, the most by a defensive tackle in team history.
A former second-round pick in 2013 out of Purdue, Short has started 32 games the last two seasons and 41 overall.
He has 22 sacks, 88 quarterback pressures, six forced fumbles, five recoveries and 13 passes defended.
Panthers head coach Ron Rivera went into detail on Short's value to the team earlier this month.
"We believe up front is the most important part of your team," Rivera told ESPN's NFL Insiders. "You've got to be able to stop the run, rush the passer, and I think KK is one of those guys who has that kind of ability.
"We've gone through some of our salary cap meetings already," Rivera said. "(General manager) Dave Gettleman and his staff has looked at it, and the best way to approach KK as we get into free agency is obviously, we're probably going to have to tag him. If we do, so be it. If not, I think they can get a deal done and I'm pretty optimistic about that.
"KK is a big part of what we do."
The move to franchise Short comes less than 24 hours after the Panthers re-signed defensive end Mario Addison to a three-year contract and signed defensive end Horton to a two-year deal.
Addison was set to become an unrestricted free agent, while Horton would have been a restricted free agent.
Addison had a career-high amount of sacks last season for the Panthers in 2016, including eight in the final nine games, while Horton started 10 games last season and recorded 11 tackles and 2 sacks.
