Owner and general manager Jerry Jones spoke with Roosevelt Barnes on Thursday evening and the two agreed to talk again before the March 5 deadline the team faces on whether to use the franchise tag.
Barnes said the talks were preliminary and he expressed hope that a long-term contract extension could be worked out.
Executive vice president Stephen Jones said Wednesday that the team has not decided whether to use the tag and did not rule out the possibility of a multi-year deal.
The franchise tag would cost the Cowboys $8.8 million.
Head coach Jason Garrett indicated Thursday that the Cowboys are still looking at their options.
"We just have to continue to talk about it and figure out what we want to do," Garrett said. "We've had a lot of discussions on this topic right now. We have some time to do it. Anthony Spencer has been a very good player for us and we have some different options that we can explore and that we've talked about. We're not ready to make that decision. We don't have to make it yet. But you have to evaluate the landscape of how you can acquire talent. You have to look at who's available in the draft, who's available in free agency and who's available on your team, and then you try to make your best decision. We're just not there yet with Spence."
Spencer, a first-round pick in 2007, has never had more than six sacks in a season. He has 21.5 sacks for his career and has started 47 of the last 48 games since taking over for Greg Ellis in 2009.
Jones said the Cowboys do not have an in-house replacement for Spencer and that even if they tagged Spencer it would not preclude them from taking an outside linebacker in the first round of the April draft.