By signing the tender, Spencer will be guaranteed to make at least
$10.6 million in 2013, but two options remain: He could sign a multiyear deal with the Cowboys or he could be traded.
The sides have until July 15 to work out a deal, or Spencer will play the year on the tag.
"We've got a little time, but I told them I'd like to start moving forward on this and hopefully maybe as soon as next week we can have some serious talks toward it," Woy said about a long-term deal.
Spencer's preference is to remain with the team that drafted him in the first round in 2007. Spencer led the Cowboys in tackles last year (106), established a career high in sacks (11) and was named to his first Pro Bowl.
Spencer made $8.8 million last season as the Cowboys' franchise player.
With the Cowboys' move to a 4-3 defense under new coordinator Monte Kiffin, Spencer will move to defensive end. He played the position in college, but owner and general manager Jerry Jones said during the NFL scouting combine last month that Spencer might not have the preferred size for the position.
Dallas also offered safety Danny McCray, its only restricted free agent, a one-year tender worth $1.3 million on Friday.