But the Pro Bowl inside linebacker could be laying the groundwork to go elsewhere when free agency begins Friday.
"When we played Ray Lewis and Baltimore at the end of the season, he came over and pointed to my helmet. He said: 'I want to wear this star on my helmet. That's my dream ... that's my dream,' " Ware told the Cowboys' official Web site. "When we got to the Pro Bowl, he did it again. He came at me every day. He's trying to get down where the star is. He told me he needed me to get him [owner] Jerry Jones' phone number for him. I just busted out laughing."
If the Ravens cannot reach a new contract with Lewis in four days, he will become a free agent for the first time in his 13-year career.
While Lewis might be targeting Dallas, the feeling might not be mutual. The Cowboys are reportedly $10 million under the salary cap and likely will use most of that in signing Ware to a franchise-record contract.
Ware, who led the NFL with 20 sacks last season, said he doesn't believe Lewis is using the Cowboys as leverage against the Ravens.
"Believe me, he is genuine," Ware told the Cowboys' Web site. "He talked to me two years ago about it. He calls me about once a week and talks about it then. I even said: 'Hey, Ray, I'm tired about talking about this. You need to find Jerry Jones' number and fly out there and talk to him.' "