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As the story goes, Trey Griffey had a contract offer from the Seattle Mariners — post-dated for 2012 — not long after he was born in 1994.

Nineteen years later, The Kid’s kid is instead an up-and-coming wide receiver on an up-and-coming Pac-12 Conference team.

“I still have a lot to improve on,” Trey Griffey said in a phone interview from Tucson, Ariz., where he’s a redshirt freshman in Rich Rodriguez’s Arizona offense. “I just want to be somebody who fits in here. And when I have a chance to make a play, I want to make the play.”

Griffey, listed at 6 feet 3, 190 pounds, was a three-star recruit out of Orlando, Fla., after catching 73 passes for 970 yards and 11 touchdowns in 12 games as a senior at Dr. Phillips High School. He played in the 2012 Under Armour All-American game and soon after chose to sign with Arizona, spurning offers from Washington State, Michigan State and Iowa State, among others.

The Griffey family’s ties to Arizona were strengthened when Trey’s younger sister — and daughter of Ken Jr. and Melissa — committed to play basketball at Arizona earlier this summer. Taryn Griffey is ranked as the nation’s No. 45 women’s basketball recruit by ESPN for the Class of 2014.

“It’ll be great to see my little sister every day,” Griffey said.

Griffey didn’t get to see his dad’s introduction into the Mariners’ Hall of Fame two weeks ago. The Wildcats had a scrimmage right about the same time. But Griffey taped a message that played at Safeco Field during his dad’s ceremony. It brought Junior to tears.

“My mom told me about that,” Trey Griffey said. “And I talked to him afterward.”

It remains to be seen whether Griffey will have a chance to contribute for the Wildcats this season, but he said he is making strides in his second year in Rodriguez’s up-tempo offense.

“Everything is starting to slow down,” Trey Griffey said. “In my first year, there was a little shock at the speed jump from high school. … I’m definitely getting better at understanding the plays and recognizing defenses.”

Arizona receivers coach Tony Dews told the Tucson Citizen that Griffey is “coming along.”

“He’s not making very many mental errors anymore,” Dews said. “He’s doing a really good job, assignment-wise. His hands have continued to develop, although he already had good ball skills coming in.

“You continue to see signs that, man, we’ve got a guy who can catch the ball no matter where you throw it.”

The biggest mystery for the Wildcats is which quarterback will be throwing the ball to the receivers this season. Senior B.J. Denker, a lefty, is the front-runner; he’s the only quarterback with experience — albeit limited — in Rodriguez’s system. He started in place of the departed Matt Scott against Colorado last season, completing 25 of 37 passes for 259 yards with three touchdowns and one interception.

The other quarterback candidate is Jesse Scroggins, a junior-college transfer who originally signed with USC.

“We might not decide until the season,” Rodriguez told reporters earlier this week.

Whoever the quarterback is, he will have the luxury of throwing to the nation’s top running back, Ka’Deem Carey, whose 1,929 yards and 23 touchdowns carried the Wildcats to an 8-5 finish in Rodriguez’s first season. That included a thrilling 49-48 victory over Nevada in the New Mexico Bowl.

On defense, Arizona was last in the Pac-12 — yes, even worse than Colorado — in allowing 499 yards per game last season. Rodriguez is confident the defense will improve.

“Our guys never quit,” he said. “They battled through tough times defensively and we knew we were hanging on a little bit. I like what we do defensively and I like the players coming back.”

Adam Jude: 206-464-2364 or