The Diamondbacks have identified Brandon Webb as a long-term priority and have renewed talks on a contract extension that would keep the pitcher through the prime of his career, and Webb seems to believe a new deal can be reached.

“We’ve been talking a little bit and, hopefully, it’s not something that drags out too long,” Webb said after pitching his first complete game of a season in an 8-3 victory over Philadelphia Thursday.

“We’ll get something done.”

Webb, 8-0 for the second time in three years, is one of the best values in the major leagues — he is to earn $5.5 million this season and $6.5 million in 2009, and the D-Backs have an option worth $8.5 million with a $1.5 million buyout in 2010.

The D-Backs made an offer that Webb rejected last December, and the sides have been working intermittently, out of the public eye, on a deal.

D-Backs general manager Josh Byrnes and Webb’s agent, Jonathan Maurer, did not comment, although Maurer said at the winter meetings that he did not want to “break the bank,” as he put it, and was seeking “a fair deal.”

The D-Backs, sources said, are not prepared to offer Johan Santana-type money — he signed a six-year extension worth almost $23 million a year after being traded to the Mets — but understand they will need to make a significant commitment.

Randy Johnson’s contract expires after this season, which will free $16 million.

If the D-Backs follow form showed in previous extensions, they would offer Webb an extension of at least three more years at a price that would offer Webb immediate security and give the D-Backs cost certainty and a hedge against future inflationary market forces.

DAVIS ALMOST CANCER FREE

Doug Davis’ thyroid cancer has not spread, and soon he could be cancer free.

A nuclear CT scan revealed the good news on Thursday morning. Radiation iodine pills are expected to take care of the rest of the cancer.

“I shook Dr. (Bob) Evani’s hand and told him what a great job he did,” Davis said. “I hugged my fiancee, then we got out of there. Nobody wants to stay in the doctor’s office longer than they have to.”

Davis will make a rehab start Saturday and then another on Thursday at Triple-A Tucson. He would likely return to the big leagues after the second start if there are no setbacks. That would put him on schedule to be back on May 20 in Florida.

INJURY UPDATE

Orlando Hudson (hamstring) and Conor Jackson (head) were both absent from Thursday’s lineup, although manager Bob Melvin said before the game that both were available for pinch-hitting duties. But neither played in the game.

Hudson will be available for pinch-hitting duties again today and Melvin said he could start on Saturday against the Cubs.

Jackson will be back in the lineup today after sitting out following a collision at first base with Shane Victorino in the eighth inning Wednesday.

“I never lost consciousness, but I was definitely seeing stars,” Jackson said.

CLEANING UP

Justin Upton batted cleanup for the first time in his major league career Thursday, hitting a solo homer in the bottom of the seventh.

He is hitting .344 this year with six homers and 17 RBIs, although it was Jackson’s absence that likely facilitated the move.

ON A ROLL

Chris Snyder had just one multi-hit game by the end of April, when his average sat just above the Mendoza line at .206. Already in May he’s had four, including a 2-for-4 day on Thursday.