However, the pair of free agents have at least seven teams, in addition to the Cowboys, interested in their services.
Hatcher is coming off a 2013 season in which he set career highs in sacks (11), solo tackles (34) and tackles for loss (8).
When the season ended, Hatcher said he expected to sign a big-money deal as a free agent.
Spencer played in just one game because of knee problems, a Week 2 loss at Kansas City where he participated in 34 snaps, getting two tackles and one quarterback hit.
His knee woes continued, and he underwent microfracture surgery. For Spencer to get any type of free-agent deal, he needs to prove he can return from the surgery and be ready at the start of training camp in July.
The Cowboys have depth concerns along the defensive line with Hatcher and Spencer hitting the free-agent market.
Defensive end DeMarcus Ware could be released, creating $7.4 million in salary-cap space, which opens more holes along a defensive line that failed to get a consistent pass rush in 2013.
The Cowboys would like Ware, Spencer and Hatcher to play with the team in 2014, but finances could be problematic.
Dallas has roughly $2 million in cap space available, which is not enough to keep all three. But if the Cowboys get more cap room from Ware (due to a pay cut or a restructure) and Spencer signs to a lower salary, they both could be retained.
Hatcher is another story. He might want a salary in the $8 million to $10 million range.