The Cowboys placed an $8.8 million franchise tag on Spencer last March, and he rewarded the front office with 11 sacks and a team-leading 95 tackles in a 3-4 scheme that made the most of his talents.
The switch to coordinator Monte Kiffin's 4-3 front will likely push Spencer to defensive end, but his agent, Jordan Woy, said the move would be embraced, adding that Dallas remains Spencer's "first choice."
With the Cowboys sitting roughly $20 million over the cap, Jones acknowledged Spencer's future with the team isn't set in stone.
"Unfortunately, you've got to make difficult decisions," Jones said. "What that will entail we don't know quite yet. We'll be moving forward in a quick way. But obviously Anthony Spencer represents everything we want to be about. He plays hard. His leadership is tremendous. And then on top of that, he's a great football player."
Follow Marc Sessler on Twitter @MarcSesslerNFL.